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Artículos de revistas sobre el tema "Ornstein-Uhlenbeck process"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 25 de julio de 2025

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1

Hidayat, Amam Taufiq, and Subanar Subanar. "PERSAMAAN DIFERENSIAL ORNSTEIN-UHLENBECK DALAM PERAMALAN HARGA SAHAM." MEDIA STATISTIKA 13, no. 1 (2020): 60–67. http://dx.doi.org/10.14710/medstat.13.1.60-67.

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Geometric Brownian motion is one of the most widely used stock price model. One of the assumptions that is filled with stock return volatility is constant. Gamma Ornstein-Uhlenbeck process a model to describe volatility in finance. Additionally, Gamma Ornstein-Uhlenbeck process driven by Background Driving Levy Process (BDLP) compound Poisson process and the marginal law of volatility follows a Gamma distribution. Barndorff-Nielsen and Shepard (BNS) Gamma Ornstein-Uhlenbeck model can to sample the process for the stock price with volatility follows Gamma Ornstein-Uhlenbeck process. Based on th

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2

Pedersen, Jan. "Periodic Ornstein-Uhlenbeck processes driven by Lévy processes." Journal of Applied Probability 39, no. 4 (2002): 748–63. http://dx.doi.org/10.1239/jap/1037816016.

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In this paper, the class of periodic Ornstein-Uhlenbeck processes is defined. It is shown that periodic Ornstein-Uhlenbeck processes are stationary Markov random fields and the class of stationary distributions is characterized. In particular, any self-decomposable distribution is the stationary distribution of some periodic Ornstein-Uhlenbeck process. As examples, gamma periodic Ornstein-Uhlenbeck processes and Gaussian periodic Ornstein-Uhlenbeck processes are considered.

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3

Pedersen, Jan. "Periodic Ornstein-Uhlenbeck processes driven by Lévy processes." Journal of Applied Probability 39, no. 04 (2002): 748–63. http://dx.doi.org/10.1017/s0021900200022014.

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In this paper, the class of periodic Ornstein-Uhlenbeck processes is defined. It is shown that periodic Ornstein-Uhlenbeck processes are stationary Markov random fields and the class of stationary distributions is characterized. In particular, any self-decomposable distribution is the stationary distribution of some periodic Ornstein-Uhlenbeck process. As examples, gamma periodic Ornstein-Uhlenbeck processes and Gaussian periodic Ornstein-Uhlenbeck processes are considered.

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4

Liu, Cheng-Shi. "Ornstein–Uhlenbeck process, Cauchy process, and Ornstein–Uhlenbeck–Cauchy process on a circle." Applied Mathematics Letters 26, no. 9 (2013): 957–62. http://dx.doi.org/10.1016/j.aml.2013.04.009.

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5

Debbasch, F., K. Mallick, and J. P. Rivet. "Relativistic Ornstein–Uhlenbeck Process." Journal of Statistical Physics 88, no. 3/4 (1997): 945–66. http://dx.doi.org/10.1023/b:joss.0000015180.16261.53.

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6

Borodin, A. N. "Hyperbolic Ornstein–Uhlenbeck Process." Journal of Mathematical Sciences 219, no. 5 (2016): 631–38. http://dx.doi.org/10.1007/s10958-016-3135-0.

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7

Garbaczewski, Piotr, and Robert Olkiewicz. "Ornstein–Uhlenbeck–Cauchy process." Journal of Mathematical Physics 41, no. 10 (2000): 6843. http://dx.doi.org/10.1063/1.1290054.

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8

Bishwal, Jaya P. N. "Minimum Contrast Estimation in Fractional Ornstein-Uhlenbeck Driven by Fractional Ornstein-Uhlenbeck Process." Asian Journal of Statistics and Applications 2, no. 1 (2025): 50–72. https://doi.org/10.47509/ajsa.2025.v02i01.04.

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We generalize fractional Ornstein-Uhlenbeck process whose driving term is another fractional Ornstein-Uhlenbeck process. The motivation is related to stochastic volatility model. We estimate the parameters of both processes by maximum likelihood method and minimum contrast method. We obtain strong consistency and asymptotic normality of the estimators as the time length of observation becomes large. KEYWORDS: Stochastic differential equation, fractional Brownian motion, fractional Ornstein-Uhlenbeck process, correlation, volatility, maximum likelihood estimator, minimum contrast estimator, Dur

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9

Ascione, Giacomo, Yuliya Mishura, and Enrica Pirozzi. "Time-changed fractional Ornstein-Uhlenbeck process." Fractional Calculus and Applied Analysis 23, no. 2 (2020): 450–83. http://dx.doi.org/10.1515/fca-2020-0022.

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AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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10

Zang, Qing-Pei, and Li-Xin Zhang. "A general lower bound of parameter estimation for reflected Ornstein–Uhlenbeck processes." Journal of Applied Probability 53, no. 1 (2016): 22–32. http://dx.doi.org/10.1017/jpr.2015.5.

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AbstractA reflected Ornstein–Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein–Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. Under some mild conditions, this paper is devoted to the study of the analogue of the Cramer–Rao lower bound of a general class of parameter estimation of the unknown parameter in reflected Ornstein–Uhlenbeck processes.

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11

Setyorini, Elisabeth Yeyen, and Endah R. M. Putri. "RAINFALL MODELLING IN EAST JAVA USING A MODIFIED ORNSTEIN-UHLENBECK MODEL." Jurnal Matematika UNAND 14, no. 1 (2025): 46. https://doi.org/10.25077/jmua.14.1.46-61.2025.

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One of the current global issues is climate change and weather variability. This phenomenon has real impacts on various regions, including East Java Province. East Java is experiencing increased rainfall intensity as one of the effects of climate change. High and continuous rainfall intensity can trigger disasters such as flooding, which has the potential to cause significant financial losses for the community. Therefore, effective risk management becomes crucial. One possible solution to address these risks is through the use of financial derivatives. The initial step in risk management invol

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12

Renshaw, Eric. "The discrete uhlenbeck–ornstein process." Journal of Applied Probability 24, no. 4 (1987): 908–17. http://dx.doi.org/10.2307/3214215.

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A correlated random walk is studied in which, at each stage, the velocity changes according to a first-order process. Motion is considered both with and without friction, the former situation being the discrete analogy of the Uhlenbeck–Ornstein process. Exact and limiting expressions are developed for the cumulant structures.

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13

Sykulski, Adam, Sofia Olhede, and Hanna Sykulska-Lawrence. "The elliptical Ornstein–Uhlenbeck process." Statistics and Its Interface 16, no. 1 (2023): 133–46. http://dx.doi.org/10.4310/21-sii714.

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14

fang, shizan. "On the ornstein—uhlenbeck process." Stochastics and Stochastic Reports 46, no. 3-4 (1994): 141–59. http://dx.doi.org/10.1080/17442509408833875.

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15

Renshaw, Eric. "The discrete uhlenbeck–ornstein process." Journal of Applied Probability 24, no. 04 (1987): 908–17. http://dx.doi.org/10.1017/s002190020011678x.

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A correlated random walk is studied in which, at each stage, the velocity changes according to a first-order process. Motion is considered both with and without friction, the former situation being the discrete analogy of the Uhlenbeck–Ornstein process. Exact and limiting expressions are developed for the cumulant structures.

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16

Gajda, Janusz, and Agnieszka Wyłomańska. "Time-changed Ornstein–Uhlenbeck process." Journal of Physics A: Mathematical and Theoretical 48, no. 13 (2015): 135004. http://dx.doi.org/10.1088/1751-8113/48/13/135004.

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17

Cáceres, Manuel O., and Adrián A. Budini. "The generalized Ornstein - Uhlenbeck process." Journal of Physics A: Mathematical and General 30, no. 24 (1997): 8427–44. http://dx.doi.org/10.1088/0305-4470/30/24/009.

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18

Sykulski, Adam, Sofia Olhede, and Hanna Sykulska-Lawrence. "The elliptical Ornstein–Uhlenbeck process." Statistics and Its Interface 16, no. 1 (2023): 133–46. http://dx.doi.org/10.4310/sii.2023.v16.n1.a11.

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19

Wenocur, Michael L. "Ornstein–Uhlenbeck process with quadratic killing." Journal of Applied Probability 27, no. 3 (1990): 707–12. http://dx.doi.org/10.2307/3214554.

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An Ornstein-Uhlenbeck process subject to a quadratic killing rate is analyzed. The distribution for the process killing time is derived, generalizing the analogous result for Brownian motion. The derivation involves the use of Hermite polynomials in a spectral expansion.

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20

Eab, Chai Hok, and S. C. Lim. "Ornstein–Uhlenbeck process with fluctuating damping." Physica A: Statistical Mechanics and its Applications 492 (February 2018): 790–803. http://dx.doi.org/10.1016/j.physa.2017.11.010.

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21

Wenocur, Michael L. "Ornstein–Uhlenbeck process with quadratic killing." Journal of Applied Probability 27, no. 03 (1990): 707–12. http://dx.doi.org/10.1017/s0021900200039243.

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An Ornstein-Uhlenbeck process subject to a quadratic killing rate is analyzed. The distribution for the process killing time is derived, generalizing the analogous result for Brownian motion. The derivation involves the use of Hermite polynomials in a spectral expansion.

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22

Moxnes, John F., and Kjell Hausken. "Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations." Advances in Mathematical Physics 2010 (2010): 1–42. http://dx.doi.org/10.1155/2010/509326.

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We incorporate randomness into deterministic theories and compare analytically and numerically some well-known stochastic theories: the Liouville process, the Ornstein-Uhlenbeck process, and a process that is Gaussian and exponentially time correlated (Ornstein-Uhlenbeck noise). Different methods of achieving the marginal densities for correlated and uncorrelated noise are discussed. Analytical results are presented for a deterministic linear friction force and a stochastic force that is uncorrelated or exponentially correlated.

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23

Huang, G., H. M. Jansen, M. Mandjes, P. Spreij, and K. De Turck. "Markov-modulated Ornstein–Uhlenbeck processes." Advances in Applied Probability 48, no. 1 (2016): 235–54. http://dx.doi.org/10.1017/apr.2015.15.

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Abstract In this paper we consider an Ornstein–Uhlenbeck (OU) process (M(t))t≥0 whose parameters are determined by an external Markov process (X(t))t≥0 on a finite state space {1, . . ., d}; this process is usually referred to as Markov-modulated Ornstein–Uhlenbeck. We use stochastic integration theory to determine explicit expressions for the mean and variance of M(t). Then we establish a system of partial differential equations (PDEs) for the Laplace transform of M(t) and the state X(t) of the background process, jointly for time epochs t = t1, . . ., tK. Then we use this PDE to set up a rec

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24

Ricciardi, L. M., and L. Sacerdote. "On the probability densities of an Ornstein–Uhlenbeck process with a reflecting boundary." Journal of Applied Probability 24, no. 2 (1987): 355–69. http://dx.doi.org/10.2307/3214260.

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We show that the transition p.d.f. of the Ornstein–Uhlenbeck process with a reflection condition at an assigned state S is related by integral-type equations to the free transition p.d.f., to the transition p.d.f. in the presence of an absorption condition at S, to the first-passage-time p.d.f. to S and to the probability current. Such equations, which are also useful for computational purposes, yield as an immediate consequence all known closed-form results for Wiener and Ornstein–Uhlenbeck processes.

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25

Ricciardi, L. M., and L. Sacerdote. "On the probability densities of an Ornstein–Uhlenbeck process with a reflecting boundary." Journal of Applied Probability 24, no. 02 (1987): 355–69. http://dx.doi.org/10.1017/s0021900200031004.

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We show that the transition p.d.f. of the Ornstein–Uhlenbeck process with a reflection condition at an assigned state S is related by integral-type equations to the free transition p.d.f., to the transition p.d.f. in the presence of an absorption condition at S, to the first-passage-time p.d.f. to S and to the probability current. Such equations, which are also useful for computational purposes, yield as an immediate consequence all known closed-form results for Wiener and Ornstein–Uhlenbeck processes.

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26

Bishwal, Jaya P. N. "Quantile estimation in fractional Levy Ornstein-Uhlenbeck processes." Model Assisted Statistics and Applications 18, no. 4 (2023): 279–93. http://dx.doi.org/10.3233/mas-221427.

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First we study estimation of the drift parameter in the fractional Ornstein-Uhlenbeck process whose marginal distribution is Student t-distribution. We obtain Spearman’s correlation based estimator, quantile estimator and Brownian excursion based estimator of the drift parameter. Then we study method of moments estimator and quantile estimator in fractional inverse Gaussian and fractional gamma Ornstein-Uhlenbeck processes.

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27

Mao, Yong-Hua, and Tao Wang. "Lyapunov-type conditions for non-strong ergodicity of Markov processes." Journal of Applied Probability 58, no. 1 (2021): 238–53. http://dx.doi.org/10.1017/jpr.2020.84.

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AbstractWe present Lyapunov-type conditions for non-strong ergodicity of Markov processes. Some concrete models are discussed, including diffusion processes on Riemannian manifolds and Ornstein–Uhlenbeck processes driven by symmetric $\alpha$-stable processes. In particular, we show that any process of d-dimensional Ornstein–Uhlenbeck type driven by $\alpha$-stable noise is not strongly ergodic for every $\alpha\in (0,2]$.

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28

Gajda, Janusz, and Agnieszka Wyłomańska. "Asymptotic behavior of dependence measures for Ornstein-Uhlenbeck model based on long memory processes." International Journal of Advances in Engineering Sciences and Applied Mathematics 13, no. 2-3 (2021): 148–62. http://dx.doi.org/10.1007/s12572-021-00305-w.

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AbstractIn this paper, we study the long memory property of two processes based on the Ornstein-Uhlenbeck model. Their are extensions of the Ornstein-Uhlenbeck system for which in the classic version we replace the standard Brownian motion (or other L$$\acute{e}$$ e ´ vy process) by long range dependent processes based on $$\alpha -$$ α - stable distribution. One way of characterizing long- and short-range dependence of second order processes is in terms of autocovariance function. However, for systems with infinite variance the classic measure is not defined, therefore there is a need to cons

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29

BALDI, PAOLO, and CAMILLA PISANI. "SIMPLE SIMULATION SCHEMES FOR CIR AND WISHART PROCESSES." International Journal of Theoretical and Applied Finance 16, no. 08 (2013): 1350045. http://dx.doi.org/10.1142/s0219024913500453.

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We develop some simple simulation algorithms for CIR and Wishart processes. We investigate rigorously the square of a matrix valued Ornstein–Uhlenbeck process, the main idea being to split the generator and to reduce the problem to the simulation of the square of a matrix valued Ornstein–Uhlenbeck process to be added to a deterministic process. In this way, we provide a weak second-order scheme that requires only the simulation of i.i.d. Gaussian r.v.'s and simple matrix manipulations.

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30

Li, Anshui, Jiajia Wang, and Lianlian Zhou. "Parameter Estimation of Uncertain Differential Equations Driven by Threshold Ornstein–Uhlenbeck Process with Application to U.S. Treasury Rate Analysis." Symmetry 16, no. 10 (2024): 1372. http://dx.doi.org/10.3390/sym16101372.

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Uncertain differential equations, as an alternative to stochastic differential equations, have proved to be extremely powerful across various fields, especially in finance theory. The issue of parameter estimation for uncertain differential equations is the key step in mathematical modeling and simulation, which is very difficult, especially when the corresponding terms are driven by some complicated uncertain processes. In this paper, we propose the uncertainty counterpart of the threshold Ornstein–Uhlenbeck process in probability, named the uncertain threshold Ornstein–Uhlenbeck process, fil

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31

Liao, Zhongwei, and Jinghai Shao. "Long-time behavior of Lévy-driven Ornstein–Uhlenbeck processes with regime switching." Journal of Applied Probability 57, no. 1 (2020): 266–79. http://dx.doi.org/10.1017/jpr.2019.96.

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AbstractWe investigate the long-time behavior of the Ornstein–Uhlenbeck process driven by Lévy noise with regime switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein–Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Lévy noise and the regime switching described by a Markov chain can derive the heavy-tailed property of the stationary distribution. The different role played by the Lévy measure and the regime-switching process is clearly characterize

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32

Obuchowski, J., and A. Wyłomańska. "Ornstein--Uhlenbeck Process with Non-Gaussian Structure." Acta Physica Polonica B 44, no. 5 (2013): 1123. http://dx.doi.org/10.5506/aphyspolb.44.1123.

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33

Pashko, A. O., and T. O. Ianevych. "Methods for modeling the Ornstein-Uhlenbeck process." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2019): 24–29. http://dx.doi.org/10.17721/1812-5409.2019/3.3.

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Two methods of modeling for the Ornstein-Uhlenbeck process are studied in the work. This process has many applications in physics, financial mathematics, biology. Therefore, it is extremely important to have instruments for modeling this process to solve various theoretical and practical tasks. The peculiarity of this process is that it has many interesting properties: it is Gaussian process, is a stationary process, is a Markov process, it is a solution of the Langevin stochastic equation, etc. Each of these properties allows you to apply different methods to this process modeling. We have co

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34

Lewis, John Courtenay. "Pressure narrowing and the Ornstein–Uhlenbeck process." Journal of Chemical Physics 84, no. 5 (1986): 2503–13. http://dx.doi.org/10.1063/1.450837.

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35

Ruscitti, Claudia, Laura Langoni, and Augusto Melgarejo. "Description of instabilities in Uhlenbeck–Ornstein process." Physica Scripta 94, no. 11 (2019): 115010. http://dx.doi.org/10.1088/1402-4896/ab2931.

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36

Lefebvre, Mario. "Optimal control of an Ornstein-Uhlenbeck process." Stochastic Processes and their Applications 24, no. 1 (1987): 89–97. http://dx.doi.org/10.1016/0304-4149(87)90030-5.

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37

Graversen, S. E., and G. Peskir. "Maximal inequalities for the Ornstein-Uhlenbeck process." Proceedings of the American Mathematical Society 128, no. 10 (2000): 3035–42. http://dx.doi.org/10.1090/s0002-9939-00-05345-4.

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38

Mariani, Maria, Peter Asante, William Kubin, and Osei Tweneboah. "Data Analysis Using a Coupled System of Ornstein–Uhlenbeck Equations Driven by Lévy Processes." Axioms 11, no. 4 (2022): 160. http://dx.doi.org/10.3390/axioms11040160.

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In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a predictive model. There’s empirical evidence showing that there exist dependencies or correlations between events; thus, we may be able to model them together. Here we show such correlation between data from finance, geophysics and health as well as show the predictive performance when they are modeled with a coupled Ornstein–Uhlenbeck system of

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39

Giorgini, L. T., W. Moon, and J. S. Wettlaufer. "Analytical Survival Analysis of the Ornstein–Uhlenbeck Process." Journal of Statistical Physics 181, no. 6 (2020): 2404–14. http://dx.doi.org/10.1007/s10955-020-02669-y.

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AbstractWe use asymptotic methods from the theory of differential equations to obtain an analytical expression for the survival probability of an Ornstein–Uhlenbeck process with a potential defined over a broad domain. We form a uniformly continuous analytical solution covering the entire domain by asymptotically matching approximate solutions in an interior region, centered around the origin, to those in boundary layers, near the lateral boundaries of the domain. The analytic solution agrees extremely well with the numerical solution and takes into account the non-negligible leakage of probab

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40

Cui, Jingwen, Hao Liu, and Xiaohui Ai. "Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck process." AIMS Mathematics 9, no. 12 (2024): 34981–5003. https://doi.org/10.3934/math.20241665.

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<p>This paper studied a stochastic fear effect predator-prey model with Crowley-Martin functional response and the Ornstein-Uhlenbeck process. First, the biological implication of introducing the Ornstein-Uhlenbeck process was illustrated. Subsequently, the existence and uniqueness of the global solution were then established. Moreover, the ultimate boundedness of the model was analyzed. Then, by constructing the Lyapunov function and applying $ It\hat{o} $'s formula, the existence of the stationary distribution of the model was demonstrated. In addition, sufficient conditions for specie

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41

Khalaf, Anas D., Anwar Zeb, Tareq Saeed, Mahmoud Abouagwa, Salih Djilali, and Hashim M. Alshehri. "A Special Study of the Mixed Weighted Fractional Brownian Motion." Fractal and Fractional 5, no. 4 (2021): 192. http://dx.doi.org/10.3390/fractalfract5040192.

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In this work, we present the analysis of a mixed weighted fractional Brownian motion, defined by ηt:=Bt+ξt, where B is a Brownian motion and ξ is an independent weighted fractional Brownian motion. We also consider the parameter estimation problem for the drift parameter θ>0 in the mixed weighted fractional Ornstein–Uhlenbeck model of the form X0=0;Xt=θXtdt+dηt. Moreover, a simulation is given of sample paths of the mixed weighted fractional Ornstein–Uhlenbeck process.

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42

Bercu, Bernard, and Adrien Richou. "Large deviations for the Ornstein-Uhlenbeck process with shift." Advances in Applied Probability 47, no. 3 (2015): 880–901. http://dx.doi.org/10.1239/aap/1444308886.

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We investigate the large deviation properties of the maximum likelihood estimators for the Ornstein-Uhlenbeck process with shift. We propose a new approach to establish large deviation principles which allows us, via a suitable transformation, to circumvent the classical nonsteepness problem. We estimate simultaneously the drift and shift parameters. On the one hand, we prove a large deviation principle for the maximum likelihood estimates of the drift and shift parameters. Surprisingly, we find that the drift estimator shares the same large deviation principle as the estimator previously esta

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43

Bercu, Bernard, and Adrien Richou. "Large deviations for the Ornstein-Uhlenbeck process with shift." Advances in Applied Probability 47, no. 03 (2015): 880–901. http://dx.doi.org/10.1017/s0001867800048874.

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We investigate the large deviation properties of the maximum likelihood estimators for the Ornstein-Uhlenbeck process with shift. We propose a new approach to establish large deviation principles which allows us, via a suitable transformation, to circumvent the classical nonsteepness problem. We estimate simultaneously the drift and shift parameters. On the one hand, we prove a large deviation principle for the maximum likelihood estimates of the drift and shift parameters. Surprisingly, we find that the drift estimator shares the same large deviation principle as the estimator previously esta

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44

Csörgő, Miklós, and Lajos Horváth. "Invariance principles for logarithmic averages." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 1 (1992): 195–205. http://dx.doi.org/10.1017/s0305004100070870.

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AbstractWe obtain weak and strong Gaussian approximations for logarithmic averages of indicators of normalized partial sums. The proofs are based on invariance principles for integrals of an Ornstein–Uhlenbeck process and on strong approximations of normalized partial sums by Orstein–Uhlenbeck processes.

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45

Ianevych, Tetiana, Olga Vasylyk, and Julia DOSHCHUK. "On modeling gaussian stationary Ornstein–Uhlenbeck processes with given reliability and accuracy in Lp-spaces." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2024): 51–56. http://dx.doi.org/10.17721/1812-5409.2024/1.9.

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Even though the problem of modelling and simulation is not new it continues to be actual over time. Our computers are becoming more powerful and this allows us to use more sofisticated algorithms for more complicated problems. In this paper we constructed the model from the series decomposition of the Gaussian stationary Ornstein–Uhlenbeck process. The Ornstein-Uhlenbeck process is widely used to model reversal processes, exchange rates, asset price volatility, etc. Controlling the model’s accuracy and reliability with which it approximates the real process is important for applications. For t

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46

Nabati, Parisa, and Arezoo Hajrajabi. "Three-factor mean reverting Ornstein-Uhlenbeck process with stochastic drift term innovations: Nonlinear autoregressive approach with dependent error." Filomat 36, no. 7 (2022): 2345–55. http://dx.doi.org/10.2298/fil2207345n.

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This paper introduces a novel approach, withen the context of energy market, by employing a three-factor mean reverting Ornstein-Uhlenbeck process with a stochastic nonlinear autoregressive drift term having a dependent error. Initially the unique solvability for the given nonlinear system is investigated. Then, to estimate the nonlinear regression function, a semiparametric method, based on the conditional least square estimator for the parametric approach, and the nonparametric kernel method for autoregressive modification estimation have been presented . A maximum likelihood estimator has b

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47

AHLIP, REHEZ. "FOREIGN EXCHANGE OPTIONS UNDER STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES." International Journal of Theoretical and Applied Finance 11, no. 03 (2008): 277–94. http://dx.doi.org/10.1142/s0219024908004804.

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In this paper, we present a stochastic volatility model with stochastic interest rates in a Foreign Exchange (FX) setting. The instantaneous volatility follows a mean-reverting Ornstein–Uhlenbeck process and is correlated with the exchange rate. The domestic and foreign interest rates are modeled by mean-reverting Ornstein–Uhlenbeck processes. The main result is an analytic formula for the price of a European call on the exchange rate. It is derived using martingale methods in arbitrage pricing of contingent claims and Fourier inversion techniques.

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48

Bishwal, Jaya P. N. "On the Kolmogorov Distance for the Least Squares Estimator in the Fractional Ornstein-Uhlenbeck Process." European Journal of Mathematical Analysis 3 (March 3, 2023): 14. http://dx.doi.org/10.28924/ada/ma.3.14.

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The paper shows that the distribution of the normalized least squares estimator of the drift parameter in the fractional Ornstein-Uhlenbeck process observed over [0, T] converges to the standard normal distribution with an uniform optimal error bound of the order O(T −1/2) for 0.5 ≤ H ≤ 0.63 and of the order O(T4H-3) for 0.63 < H < 0.75 where H is the Hurst exponent of the fractional Brownian motion driving the Ornstein-Uhlenbeck process. For the normalized quasi-least squares estimator, the error bound is of the order O(T−1/4) for 0.5 ≤ H ≤ 0.69 and of the order O(T4H−3) for 0.69 < H

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49

Song, Yajun, Ruyue Hu, Yifan Wu, and Xiaohui Ai. "Analysis of a stochastic two-species Schoener's competitive model with Lévy jumps and Ornstein–Uhlenbeck process." AIMS Mathematics 9, no. 5 (2024): 12239–58. http://dx.doi.org/10.3934/math.2024598.

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<abstract><p>This paper studies a stochastic two-species Schoener's competitive model with Lévy jumps by the mean-reverting Ornstein–Uhlenbeck process. First, the biological implication of introducing the Ornstein–Uhlenbeck process is illustrated. After that, we show the existence and uniqueness of the global solution. Moment estimates for the global solution of the stochastic model are then given. Moreover, by constructing the Lyapunov function and applying Itô's formula and Chebyshev's inequality, it is found that the model is stochastic and ultimately bounded. In addition, we gi

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50

Eliazar, Iddo. "Levy Noise Affects Ornstein–Uhlenbeck Memory." Entropy 27, no. 2 (2025): 157. https://doi.org/10.3390/e27020157.

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This paper investigates the memory of the Ornstein–Uhlenbeck process (OUP) via three ratios of the OUP increments: signal-to-noise, noise-to-noise, and tail-to-tail. Intuition suggests the following points: (1) changing the noise that drives the OUP from Gauss to Levy will not affect the memory, as both noises share the common `independent increments’ property; (2) changing the auto-correlation of the OUP from exponential to slowly decaying will affect the memory, as the change yields a process with long-range correlations; and (3) with regard to Levy driving noise, the greater the noise fluct

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