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Journal articles on the topic 'Lévy-Type Processes'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Wagner, Vanja. "Censored symmetric Lévy-type processes." Forum Mathematicum 31, no. 6 (2019): 1351–68. http://dx.doi.org/10.1515/forum-2018-0076.

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AbstractWe examine three equivalent constructions of a censored symmetric purely discontinuous Lévy process on an open set D; via the corresponding Dirichlet form, through the Feynman–Kac transform of the Lévy process killed outside of D and from the same killed process by the Ikeda–Nagasawa–Watanabe piecing together procedure. By applying the trace theorem on n-sets for Besov-type spaces of generalized smoothness associated with complete Bernstein functions satisfying certain scaling conditions, we analyze the boundary behavior of the corresponding censored Lévy process and determine conditio

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2

Sandrić, Nikola. "Ergodicity of Lévy-Type Processes." ESAIM: Probability and Statistics 20 (2016): 154–77. http://dx.doi.org/10.1051/ps/2016009.

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3

Sandrić, Nikola. "On transience of Lévy-type processes." Stochastics 88, no. 7 (2016): 1012–40. http://dx.doi.org/10.1080/17442508.2016.1178749.

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4

Wang, Jie-Ming. "Stochastic Comparison for Lévy-Type Processes." Journal of Theoretical Probability 26, no. 4 (2011): 997–1019. http://dx.doi.org/10.1007/s10959-011-0394-z.

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5

Krühner, Paul, and Alexander Schnurr. "Time change equations for Lévy-type processes." Stochastic Processes and their Applications 128, no. 3 (2018): 963–78. http://dx.doi.org/10.1016/j.spa.2017.06.011.

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6

Asmussen, Søren. "Lévy Processes, Phase-Type Distributions, and Martingales." Stochastic Models 30, no. 4 (2014): 443–68. http://dx.doi.org/10.1080/15326349.2014.958424.

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7

Dieker, A. B. "Applications of factorization embeddings for Lévy processes." Advances in Applied Probability 38, no. 03 (2006): 768–91. http://dx.doi.org/10.1017/s0001867800001269.

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We give three applications of the Pecherskii-Rogozin-Spitzer identity for Lévy processes. First, we find the joint distribution of the supremum and the epoch at which it is ‘attained’ if a Lévy process has phase-type upward jumps. We also find the characteristics of the ladder process. Second, we establish general properties of perturbed risk models, and obtain explicit fluctuation identities in the case that the Lévy process is spectrally positive. Third, we study the tail asymptotics for the supremum of a Lévy process under different assumptions on the tail of the Lévy measure.

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8

Dieker, A. B. "Applications of factorization embeddings for Lévy processes." Advances in Applied Probability 38, no. 3 (2006): 768–91. http://dx.doi.org/10.1239/aap/1158685001.

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We give three applications of the Pecherskii-Rogozin-Spitzer identity for Lévy processes. First, we find the joint distribution of the supremum and the epoch at which it is ‘attained’ if a Lévy process has phase-type upward jumps. We also find the characteristics of the ladder process. Second, we establish general properties of perturbed risk models, and obtain explicit fluctuation identities in the case that the Lévy process is spectrally positive. Third, we study the tail asymptotics for the supremum of a Lévy process under different assumptions on the tail of the Lévy measure.

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9

Li, Zeng-Hu. "Ornstein-Uhlenbeck type processes and branching processes with immigration." Journal of Applied Probability 37, no. 03 (2000): 627–34. http://dx.doi.org/10.1017/s0021900200015862.

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It is shown that an Ornstein-Uhlenbeck type process associated with a spectrally positive Lévy process can be obtained as the fluctuation limits of both discrete state and continuous state branching processes with immigration.

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10

Li, Zeng-Hu. "Ornstein-Uhlenbeck type processes and branching processes with immigration." Journal of Applied Probability 37, no. 3 (2000): 627–34. http://dx.doi.org/10.1239/jap/1014842823.

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It is shown that an Ornstein-Uhlenbeck type process associated with a spectrally positive Lévy process can be obtained as the fluctuation limits of both discrete state and continuous state branching processes with immigration.

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11

Sandrić, Nikola. "On recurrence and transience of two-dimensional Lévy and Lévy-type processes." Stochastic Processes and their Applications 126, no. 2 (2016): 414–38. http://dx.doi.org/10.1016/j.spa.2015.09.006.

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12

Knopova, Viktorya, and René L. Schilling. "Transition Density Estimates for a Class of Lévy and Lévy-Type Processes." Journal of Theoretical Probability 25, no. 1 (2010): 144–70. http://dx.doi.org/10.1007/s10959-010-0300-0.

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13

FARKAS, WALTER, NILS REICH, and CHRISTOPH SCHWAB. "ANISOTROPIC STABLE LEVY COPULA PROCESSES — ANALYTICAL AND NUMERICAL ASPECTS." Mathematical Models and Methods in Applied Sciences 17, no. 09 (2007): 1405–43. http://dx.doi.org/10.1142/s0218202507002327.

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We consider the valuation of derivative contracts on baskets of risky assets whose prices are Lévy-like Feller processes of tempered stable type. The dependence among the marginals' jump structure is parametrized by a Lévy copula. For marginals of regular, exponential Lévy type in the sense of Ref. 7 we show that the infinitesimal generator [Formula: see text] of the resulting Lévy copula process is a pseudo-differential operator whose principal symbol is a distribution of anisotropic homogeneity. We analyze the jump measure of the corresponding Lévy copula processes. We prove that the domains

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14

Yamamuro, Kouji. "On transient Markov processes of Ornstein-Uhlenbeck type." Nagoya Mathematical Journal 149 (March 1998): 19–32. http://dx.doi.org/10.1017/s002776300000653x.

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Abstract.For Hunt processes on Rd, strong and weak transience is defined by finiteness and infiniteness, respectively, of the expected last exit times from closed balls. Under some condition, which is satisfied by Lévy processes and Ornstein-Uhlenbeck type processes, this definition is expressed in terms of the transition probabilities. A criterion is given for strong and weak transience of Ornstein-Uhlenbeck type processes on Rd, using their Lévy measures and coefficient matrices of linear drift terms. An example is discussed.

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15

Kella, Offer, and Onno Boxma. "Useful Martingales for Stochastic Storage Processes with Lévy-Type Input." Journal of Applied Probability 50, no. 02 (2013): 439–49. http://dx.doi.org/10.1017/s0021900200013474.

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In this paper we generalize the martingale of Kella and Whitt to the setting of Lévy-type processes and show that the (local) martingales obtained are in fact square-integrable martingales which upon dividing by the time index converge to zero almost surely and in L 2. The reflected Lévy-type process is considered as an example.

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16

Kella, Offer, and Onno Boxma. "Useful Martingales for Stochastic Storage Processes with Lévy-Type Input." Journal of Applied Probability 50, no. 2 (2013): 439–49. http://dx.doi.org/10.1239/jap/1371648952.

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In this paper we generalize the martingale of Kella and Whitt to the setting of Lévy-type processes and show that the (local) martingales obtained are in fact square-integrable martingales which upon dividing by the time index converge to zero almost surely and in L2. The reflected Lévy-type process is considered as an example.

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17

Aurzada, Frank, Leif Döring, and Mladen Savov. "Small time Chung-type LIL for Lévy processes." Bernoulli 19, no. 1 (2013): 115–36. http://dx.doi.org/10.3150/11-bej395.

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18

Kühn, Franziska. "Transition probabilities of Lévy-type processes: Parametrix construction." Mathematische Nachrichten 292, no. 2 (2018): 358–76. http://dx.doi.org/10.1002/mana.201700441.

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19

Kolokoltsov, Vassili N. "Nonlinear Markov Semigroups and Interacting Lévy Type Processes." Journal of Statistical Physics 126, no. 3 (2006): 585–642. http://dx.doi.org/10.1007/s10955-006-9211-y.

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20

Kosenkova, T., and A. Kulik. "Transportation distance between the Lévy measures and stochastic equations for Lévy-type processes." Modern Stochastics: Theory and Applications 1, no. 1 (2014): 49–64. http://dx.doi.org/10.15559/vmsta-2014.1.1.7.

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21

Kaleta, Kamil, and József Lőrinczi. "Typical long-time behavior of ground state-transformed jump processes." Communications in Contemporary Mathematics 22, no. 02 (2019): 1950002. http://dx.doi.org/10.1142/s0219199719500020.

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We consider a class of Lévy-type processes derived via a Doob transform from Lévy processes conditioned by a control function called potential. These ground state transformed processes (also called [Formula: see text]-processes) have position-dependent and generally unbounded components, with stationary distributions given by the ground states of the Lévy generators perturbed by the potential. We derive precise upper envelopes for the almost sure long-time behavior of these ground state-transformed Lévy processes, characterized through escape rates and integral tests. We also highlight the rol

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22

Brody, Dorje C., Lane P. Hughston, and Xun Yang. "Signal processing with Lévy information." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2149 (2013): 20120433. http://dx.doi.org/10.1098/rspa.2012.0433.

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Lévy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Lévy process admits exponential moments, then there exists a parametric family of measure changes called Esscher transformations. If the parameter is replaced with an independent random variable, the true value of which represents a ‘message’, then under the transformed measure the original Lévy process takes on the character of an ‘information process’. In this paper we develop a theory of such Lévy information processes. The underlyin

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23

Knopova, Victoria, and René L. Schilling. "On the small-time behaviour of Lévy-type processes." Stochastic Processes and their Applications 124, no. 6 (2014): 2249–65. http://dx.doi.org/10.1016/j.spa.2014.02.008.

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24

Kühn, Franziska. "Existence and estimates of moments for Lévy-type processes." Stochastic Processes and their Applications 127, no. 3 (2017): 1018–41. http://dx.doi.org/10.1016/j.spa.2016.07.008.

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25

Einmahl, Uwe. "LIL type behavior of multivariate Lévy processes at zero." Transactions of the American Mathematical Society 372, no. 9 (2019): 6437–64. http://dx.doi.org/10.1090/tran/7805.

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26

Lorig, Matthew, Stefano Pagliarani, and Andrea Pascucci. "A family of density expansions for Lévy-type processes." Annals of Applied Probability 25, no. 1 (2015): 235–67. http://dx.doi.org/10.1214/13-aap994.

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27

Bertoin, Jean. "Ergodic aspects of some Ornstein–Uhlenbeck type processes related to Lévy processes." Stochastic Processes and their Applications 129, no. 4 (2019): 1443–54. http://dx.doi.org/10.1016/j.spa.2018.05.007.

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28

Maejima, Makoto, and Ken-iti Sato. "Semi-Lévy processes, semi-selfsimilar additive processes, and semi-stationary Ornstein-Uhlenbeck type processes." Journal of Mathematics of Kyoto University 43, no. 3 (2003): 609–39. http://dx.doi.org/10.1215/kjm/1250283698.

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29

Kern, Peter, Svenja Lage, and Mark M. Meerschaert. "Semi-fractional diffusion equations." Fractional Calculus and Applied Analysis 22, no. 2 (2019): 326–57. http://dx.doi.org/10.1515/fca-2019-0021.

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Abstract It is well known that certain fractional diffusion equations can be solved by the densities of stable Lévy motions. In this paper we use the classical semigroup approach for Lévy processes to define semi-fractional derivatives, which allows us to generalize this statement to semistable Lévy processes. A Fourier series approach for the periodic part of the corresponding Lévy exponents enables us to represent semi-fractional derivatives by a Grünwald-Letnikov type formula. We use this formula to calculate semi-fractional derivatives and solutions to semi-fractional diffusion equations n

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30

Santos, Edson Bastos e., and Nelson Ithiro Tanaka. "Cópulas Dinâmicas de Lévy e suas Aplicações no Apreçamento de Opções Multidimensionais com Dependência na Trajetória." Brazilian Review of Finance 6, no. 1 (2008): 69. http://dx.doi.org/10.12660/rbfin.v6n1.2008.1234.

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This article presents an alternative to modeling multidimensional options, where the payoffs depend on the paths of the trajectories of the underlying-asset prices. The proposed technique considers Lévy processes, a very ample class of stochastic processes that allows the existence of jumps (discontinuities) in the price process of financial assets, and as a particular case, comprises the Brownian motion. To describe the dependence among Lévy processes, extending the static concepts of the ordinary copulas to the Lévy processes context, considering the Lévy measure, which characterizes the jum

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31

ACCARDI, LUIGI, ABDESSATAR BARHOUMI, and ANIS RIAHI. "WHITE NOISE LÉVY–MEIXNER PROCESSES THROUGH A TRANSFER PRINCIPAL FROM ONE-MODE TO ONE-MODE TYPE INTERACTING FOCK SPACES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 13, no. 03 (2010): 435–60. http://dx.doi.org/10.1142/s0219025710004103.

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Consider the Lévy–Meixner one-mode interacting Fock space {ΓLM, 〈 ⋅, ⋅ 〉LM}. Inspired by a derivative formula appearing in 〈 ⋅, ⋅ 〉LM, we define scalar products 〈 ⋅, ⋅ 〉LM , nin symmetric n-particle spaces. Then, we introduce a class of one-mode type interacting Fock spaces [Formula: see text] naturally associated to the one-dimensional infinitely divisible distributions with Lévy–Meixner type {μr; r > 0}. The Fourier transform in generalized joint eigenvectors of a family [Formula: see text] of Lévy–Meixner Jacobi fields provides a way to explicit a unitary isomorphism 𝔘LMbetween [Formula:

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32

LIAO, MING, and LONGMIN WANG. "LIMITING PROPERTIES OF LÉVY PROCESSES IN SYMMETRIC SPACES OF NONCOMPACT TYPE." Stochastics and Dynamics 12, no. 04 (2012): 1250001. http://dx.doi.org/10.1142/s0219493712500013.

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33

Huang, Qiao, Jinqiao Duan, and Jiang-Lun Wu. "Maximum principles for nonlocal parabolic Waldenfels operators." Bulletin of Mathematical Sciences 09, no. 03 (2019): 1950015. http://dx.doi.org/10.1142/s1664360719500152.

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As a class of Lévy type Markov generators, nonlocal Waldenfels operators appear naturally in the context of investigating stochastic dynamics under Lévy fluctuations and constructing Markov processes with boundary conditions (in particular the construction with jumps). This work is devoted to prove the weak and strong maximum principles for ‘parabolic’ equations with nonlocal Waldenfels operators. Applications in stochastic differential equations with [Formula: see text]-stable Lévy processes are presented to illustrate the maximum principles.

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34

Woerner, Jeannette H. C. "Inference in Lévy-type stochastic volatility models." Advances in Applied Probability 39, no. 02 (2007): 531–49. http://dx.doi.org/10.1017/s0001867800001877.

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Based on the concept of multipower variation we establish a class of easily computable and robust estimators for the integrated volatility, especially including the squared integrated volatility, in Lévy-type stochastic volatility models. We derive consistency and feasible distributional results for the estimators. Furthermore, we discuss the applications to time-changed CGMY, normal inverse Gaussian, and hyperbolic models with and without leverage, where the time-changes are based on integrated Cox-Ingersoll-Ross or Ornstein-Uhlenbeck-type processes. We deduce which type of market microstruct

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35

Woerner, Jeannette H. C. "Inference in Lévy-type stochastic volatility models." Advances in Applied Probability 39, no. 2 (2007): 531–49. http://dx.doi.org/10.1239/aap/1183667622.

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Based on the concept of multipower variation we establish a class of easily computable and robust estimators for the integrated volatility, especially including the squared integrated volatility, in Lévy-type stochastic volatility models. We derive consistency and feasible distributional results for the estimators. Furthermore, we discuss the applications to time-changed CGMY, normal inverse Gaussian, and hyperbolic models with and without leverage, where the time-changes are based on integrated Cox-Ingersoll-Ross or Ornstein-Uhlenbeck-type processes. We deduce which type of market microstruct

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36

Ladde, Gangarm S., and Youngsoo Seol. "Lévy-type nonlinear stochastic dynamic model, method and analysis." Stochastics and Dynamics 19, no. 05 (2019): 1950033. http://dx.doi.org/10.1142/s0219493719500333.

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In this work, we consider a prototype stochastic dynamic model for dynamic processes in biological, chemical, economic, financial, medical, military, physical and technological sciences. The dynamic model is described by Lévy-type nonlinear stochastic differential equation. The model validation is established by the usage of Lyapunov-like function. The basic innovative idea is to transform a nonlinear Lévy-type nonlinear stochastic differential into a simpler stochastic differential equation that is easily tested for the existence and uniqueness theorem. Using the nature of Lyapunov-like funct

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37

Qu, Yan, Angelos Dassios, and Hongbiao Zhao. "Efficient simulation of Lévy-driven point processes." Advances in Applied Probability 51, no. 4 (2019): 927–66. http://dx.doi.org/10.1017/apr.2019.44.

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AbstractIn this paper, we introduce a new large family of Lévy-driven point processes with (and without) contagion, by generalising the classical self-exciting Hawkes process and doubly stochastic Poisson processes with non-Gaussian Lévy-driven Ornstein–Uhlenbeck-type intensities. The resulting framework may possess many desirable features such as skewness, leptokurtosis, mean-reverting dynamics, and more importantly, the ‘contagion’ or feedback effects, which could be very useful for modelling event arrivals in finance, economics, insurance, and many other fields. We characterise the distribu

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38

Limic, Vlada. "The eternal multiplicative coalescent encoding via excursions of Lévy-type processes." Bernoulli 25, no. 4A (2019): 2479–507. http://dx.doi.org/10.3150/18-bej1060.

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39

Wang, Jie Ming. "Stochastic comparison and preservation of positive correlations for Lévy-type processes." Acta Mathematica Sinica, English Series 25, no. 5 (2009): 741–58. http://dx.doi.org/10.1007/s10114-009-7670-1.

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40

Egami, Masahiko, and Kazutoshi Yamazaki. "Phase-type fitting of scale functions for spectrally negative Lévy processes." Journal of Computational and Applied Mathematics 264 (July 2014): 1–22. http://dx.doi.org/10.1016/j.cam.2013.12.044.

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41

Deepa, R., and P. Muthukumar. "Infinite horizon mean-field type relaxed optimal control with Lévy processes." IFAC-PapersOnLine 51, no. 1 (2018): 136–41. http://dx.doi.org/10.1016/j.ifacol.2018.05.023.

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42

Ivanovs, Jevgenijs. "On scale functions for Lévy processes with negative phase-type jumps." Queueing Systems 98, no. 1-2 (2021): 3–19. http://dx.doi.org/10.1007/s11134-021-09696-w.

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43

Moser, Martin, and Robert Stelzer. "Tail behavior of multivariate lévy-driven mixed moving average processes and supOU Stochastic Volatility Models." Advances in Applied Probability 43, no. 04 (2011): 1109–35. http://dx.doi.org/10.1017/s0001867800005322.

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Multivariate Lévy-driven mixed moving average (MMA) processes of the type X t = ∬f(A, t - s)Λ(dA, ds) cover a wide range of well known and extensively used processes such as Ornstein-Uhlenbeck processes, superpositions of Ornstein-Uhlenbeck (supOU) processes, (fractionally integrated) continuous-time autoregressive moving average processes, and increments of fractional Lévy processes. In this paper we introduce multivariate MMA processes and give conditions for their existence and regular variation of the stationary distributions. Furthermore, we study the tail behavior of multivariate supOU p

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44

Moser, Martin, and Robert Stelzer. "Tail behavior of multivariate lévy-driven mixed moving average processes and supOU Stochastic Volatility Models." Advances in Applied Probability 43, no. 4 (2011): 1109–35. http://dx.doi.org/10.1239/aap/1324045701.

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Multivariate Lévy-driven mixed moving average (MMA) processes of the type Xt = ∬f(A, t - s)Λ(dA, ds) cover a wide range of well known and extensively used processes such as Ornstein-Uhlenbeck processes, superpositions of Ornstein-Uhlenbeck (supOU) processes, (fractionally integrated) continuous-time autoregressive moving average processes, and increments of fractional Lévy processes. In this paper we introduce multivariate MMA processes and give conditions for their existence and regular variation of the stationary distributions. Furthermore, we study the tail behavior of multivariate supOU pr

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45

APPLEBAUM, DAVID. "ASPECTS OF RECURRENCE AND TRANSIENCE FOR LÉVY PROCESSES IN TRANSFORMATION GROUPS AND NONCOMPACT RIEMANNIAN SYMMETRIC PAIRS." Journal of the Australian Mathematical Society 94, no. 3 (2013): 304–20. http://dx.doi.org/10.1017/s1446788713000062.

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AbstractWe study recurrence and transience for Lévy processes induced by topological transformation groups acting on complete Riemannian manifolds. In particular the transience–recurrence dichotomy in terms of potential measures is established and transience is shown to be equivalent to the potential measure having finite mass on compact sets when the group acts transitively. It is known that all bi-invariant Lévy processes acting in irreducible Riemannian symmetric pairs of noncompact type are transient. We show that we also have ‘harmonic transience’, that is, local integrability of the inve

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46

LIAO, MING. "DYNAMICAL PROPERTIES OF LÉVY PROCESSES IN LIE GROUPS." Stochastics and Dynamics 02, no. 01 (2002): 1–23. http://dx.doi.org/10.1142/s0219493702000285.

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Let ϕt be a Lévy process in a semisimple Lie group G of noncompact type regarded as a stochastic flow on a homogeneous space of G, called a G-flow. We will determine the Lyapunov exponents and the stable manifolds of ϕt, and the stationary points of an associated vector field. As examples, SL (d,R)-flows and SO (1,d)-flows on SO (d) and Sd - 1 are discussed in details.

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47

D’Elia, Marta, Qiang Du, Max Gunzburger, and Richard Lehoucq. "Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes." Computational Methods in Applied Mathematics 17, no. 4 (2017): 707–22. http://dx.doi.org/10.1515/cmam-2017-0029.

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AbstractA nonlocal convection-diffusion model is introduced for the master equation of Markov jump processes in bounded domains. With minimal assumptions on the model parameters, the nonlocal steady and unsteady state master equations are shown to be well-posed in a weak sense. Then the nonlocal operator is shown to be the generator of finite-range nonsymmetric jump processes and, when certain conditions on the model parameters hold, the generators of finite and infinite activity Lévy and Lévy-type jump processes are shown to be special instances of the nonlocal operator.

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48

Levendorskiǐ, S. Z. "PRICING OF THE AMERICAN PUT UNDER LÉVY PROCESSES." International Journal of Theoretical and Applied Finance 07, no. 03 (2004): 303–35. http://dx.doi.org/10.1142/s0219024904002463.

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We consider the American put with finite time horizon T, assuming that, under an EMM chosen by the market, the stock returns follow a regular Lévy process of exponential type. We formulate the free boundary value problem for the price of the American put, and develop the non-Gaussian analog of the method of lines and Carr's randomization method used in the Gaussian option pricing theory. The result is the (discretized) early exercise boundary and prices of the American put for all strikes and maturities from 0 to T. In the case of exponential jump-diffusion processes, a simple efficient pricin

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49

Riahi, Anis, and Amine Ettaieb. "Quantum Decomposition Associated with the q-Deformed Lévy–Meixner White Noise." Open Systems & Information Dynamics 27, no. 02 (2020): 2050011. http://dx.doi.org/10.1142/s1230161220500110.

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In this paper we start with a new detailed construction of the one-mode type q-Lévy-Meixner Fock space [Formula: see text] which serves to obtain the quantum decomposition associated with the q-deformed Lévy-Meixner white noise processes. More precisely, based on the notion of quantum decomposition and the orthogonalization of polynomials of noncommutative q-Lévy-Meixner white noise [Formula: see text], we study the chaos property of the noncommutative L2-space with respect to the vacuum expectation τ. Next, we determine the distribution of the q-Lévy-Meixner operator J(χD) = ⟨ω, χD⟩ and as a

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50

BARTUMEUS, FREDERIC. "LÉVY PROCESSES IN ANIMAL MOVEMENT: AN EVOLUTIONARY HYPOTHESIS." Fractals 15, no. 02 (2007): 151–62. http://dx.doi.org/10.1142/s0218348x07003460.

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The origin of fractal patterns is a fundamental problem in many areas of science. In ecological systems, fractal patterns show up in many subtle ways and have been interpreted as emergent phenomena related to some universal principles of complex systems. Recently, Lévy-type processes have been pointed out as relevant in large-scale animal movements. The existence of Lévy probability distributions in the behavior of relevant variables of movement, introduces new potential diffusive properties and optimization mechanisms in animal foraging processes. In particular, it has been shown that Lévy pr

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