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Journal articles on the topic 'Euler scheme for SDE'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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1

ROBINSON, JAMES C. "STABILITY OF RANDOM ATTRACTORS FOR A BACKWARDS EULER SCHEME." Stochastics and Dynamics 04, no. 02 (2004): 175–84. http://dx.doi.org/10.1142/s0219493704000997.

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This paper applies a theorem from Robinson [12] in order to show that the backwards Euler approximation [Formula: see text] of a simple stochastic ODE [Formula: see text] perturbs the attractor of the SDE in an upper semicontinuous way, i.e. that [Formula: see text]

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2

Ferreiro-Castilla, A., A. E. Kyprianou, and R. Scheichl. "An Euler–Poisson scheme for Lévy driven stochastic differential equations." Journal of Applied Probability 53, no. 1 (2016): 262–78. http://dx.doi.org/10.1017/jpr.2015.23.

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Abstract We describe an Euler scheme to approximate solutions of Lévy driven stochastic differential equations (SDEs) where the grid points are given by the arrival times of a Poisson process and thus are random. This result extends the previous work of Ferreiro-Castilla et al. (2014). We provide a complete numerical analysis of the algorithm to approximate the terminal value of the SDE and prove that the mean-square error converges with rate O(n-1/2). The only requirement of the methodology is to have exact samples from the resolvent of the Lévy process driving the SDE. Classical examples, su

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3

Kubilius, Kęstutis. "Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift." Nonlinear Analysis: Modelling and Control 25, no. 6 (2020): 1059–78. http://dx.doi.org/10.15388/namc.2020.25.20565.

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Strongly consistent and asymptotically normal estimates of the Hurst index H are obtained for stochastic differential equations (SDEs) that have a unique positive solution. A strongly convergent approximation of the considered SDE solution is constructed using the backward Euler scheme. Moreover, it is proved that the Hurst estimator preserves its properties, if we replace the solution with its approximation.

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4

Banchuin, Rawid, and Roungsan Chaisricharoen. "Vector SDE Based Stochastic Analysis of Transformer." ECTI Transactions on Computer and Information Technology (ECTI-CIT) 15, no. 1 (2021): 82–107. http://dx.doi.org/10.37936/ecti-cit.2021151.188931.

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In this research, the stochastic behaviours oftransformer have been analysed by using the stochasticdifferential equation approach where both noise in thevoltage source applied to the transformer and the randomvariations in elements and parameters of transformers havebeen considered. The resulting vector stochasticdifferential equations of the transformer have been bothanalytically and numerically solved in the Ito sense wherethe Euler-Maruyama scheme has been adopted fordetermining the numerical solutions which have been theirsample means have been used for verification. With theobtained anal

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5

Zähle, Henryk. "Weak Approximation of SDEs by Discrete-Time Processes." Journal of Applied Mathematics and Stochastic Analysis 2008 (March 23, 2008): 1–15. http://dx.doi.org/10.1155/2008/275747.

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We consider the martingale problem related to the solution of an SDE on the line. It is shown that the solution of this martingale problem can be approximated by solutions of the corresponding time-discrete martingale problems under some conditions. This criterion is especially expedient for establishing the convergence of population processes to SDEs. We also show that the criterion yields a weak Euler scheme approximation of SDEs under fairly weak assumptions on the driving force of the approximating processes.

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6

Avikainen, Rainer. "On irregular functionals of SDEs and the Euler scheme." Finance and Stochastics 13, no. 3 (2009): 381–401. http://dx.doi.org/10.1007/s00780-009-0099-7.

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7

Hutzenthaler, Martin, Arnulf Jentzen, and Peter E. Kloeden. "Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2130 (2010): 1563–76. http://dx.doi.org/10.1098/rspa.2010.0348.

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The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results extend this convergence to coefficients that grow, at most, linearly. For superlinearly growing coefficients, finite-time convergence in the strong mean-square sense remains. In this article, we answer this question to the negative and prove, for a large class of SDEs with non-globally Lipschitz continuous coefficients, that Euler’s approximation converges neither in the strong mean-square sense no

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8

Lamba, H., J. C. Mattingly, and A. M. Stuart. "An adaptive Euler-Maruyama scheme for SDEs: convergence and stability." IMA Journal of Numerical Analysis 27, no. 3 (2006): 479–506. http://dx.doi.org/10.1093/imanum/drl032.

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9

Berkaoui, Abdel, Mireille Bossy, and Awa Diop. "Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence." ESAIM: Probability and Statistics 12 (November 13, 2007): 1–11. http://dx.doi.org/10.1051/ps:2007030.

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10

Zhao, Weidong, Tao Zhou, and Tao Kong. "High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control." Communications in Computational Physics 21, no. 3 (2017): 808–34. http://dx.doi.org/10.4208/cicp.oa-2016-0056.

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AbstractThis is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751] to solve the second-order FBSDEs (2FBSDEs). The key feature of the multistep schemes is that the Euler method is used to discretize the forward SDE, which dramatically reduces the entire computational complexity. Moreover, it is shown that the usual quantities of interest (e.g., the solution tuple

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11

Crisan, D., P. Dobson, and M. Ottobre. "Uniform in time estimates for the weak error of the Euler method for SDEs and a pathwise approach to derivative estimates for diffusion semigroups." Transactions of the American Mathematical Society 374, no. 5 (2021): 3289–330. http://dx.doi.org/10.1090/tran/8301.

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We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires (i) exponential decay in time of the space-derivatives of the semigroup associated with the SDE and (ii) bounds on (some) moments of the Euler approximation. We show by means of examples (and counterexamples) how both (i) and (ii) are needed to obtain the desired result. If the weak error converges to zero uniformly in time, then convergence of ergodic averages follows as well. We also show that Lyapunov-type conditions are neither su

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12

Andersson, Adam, and Raphael Kruse. "Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition." BIT Numerical Mathematics 57, no. 1 (2016): 21–53. http://dx.doi.org/10.1007/s10543-016-0624-y.

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13

Bao, Jianhai, Xing Huang, and Chenggui Yuan. "Convergence Rate of Euler–Maruyama Scheme for SDEs with Hölder–Dini Continuous Drifts." Journal of Theoretical Probability 32, no. 2 (2018): 848–71. http://dx.doi.org/10.1007/s10959-018-0854-9.

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14

Ngo, Hoang-Long, and Dai Taguchi. "On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients." Mathematics and Computers in Simulation 161 (July 2019): 102–12. http://dx.doi.org/10.1016/j.matcom.2019.01.012.

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15

Müller-Gronbach, Thomas, and Larisa Yaroslavtseva. "On the performance of the Euler–Maruyama scheme for SDEs with discontinuous drift coefficient." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 56, no. 2 (2020): 1162–78. http://dx.doi.org/10.1214/19-aihp997.

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16

Liu, Yanghui, and Samy Tindel. "First-order Euler scheme for SDEs driven by fractional Brownian motions: The rough case." Annals of Applied Probability 29, no. 2 (2019): 758–826. http://dx.doi.org/10.1214/17-aap1374.

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17

Li, Libo, and Dai Taguchi. "On the Euler–Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients." Statistics & Probability Letters 146 (March 2019): 15–26. http://dx.doi.org/10.1016/j.spl.2018.10.017.

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18

Chassagneux, Jean-François, Antoine Jacquier, and Ivo Mihaylov. "An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients." SIAM Journal on Financial Mathematics 7, no. 1 (2016): 993–1021. http://dx.doi.org/10.1137/15m1017788.

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19

Kubilius, Kęstutis, and Aidas Medžiūnas. "Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient." Mathematics 9, no. 1 (2020): 18. http://dx.doi.org/10.3390/math9010018.

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We study a class of fractional stochastic differential equations (FSDEs) with coefficients that may not satisfy the linear growth condition and non-Lipschitz diffusion coefficient. Using the Lamperti transform, we obtain conditions for positivity of solutions of such equations. We show that the trajectories of the fractional CKLS model with β>1 are not necessarily positive. We obtain the almost sure convergence rate of the backward Euler approximation scheme for solutions of the considered SDEs. We also obtain a strongly consistent and asymptotically normal estimator of the Hurst index H&gt

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20

Bourza, Mohamed, and Mohsine Benabdallah. "Convergence rate of Euler scheme for time-inhomogeneous SDEs involving the local time of the unknown process." Stochastic Models 36, no. 3 (2020): 452–72. http://dx.doi.org/10.1080/15326349.2020.1748506.

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21

Akahori, Jirô, Masahiro Kinuya, Takashi Sawai, and Tomooki Yuasa. "An efficient weak Euler–Maruyama type approximation scheme of very high dimensional SDEs by orthogonal random variables." Mathematics and Computers in Simulation 187 (September 2021): 540–65. http://dx.doi.org/10.1016/j.matcom.2021.03.010.

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22

Bossy, Mireille, Jean-François Jabir, and Kerlyns Martínez. "On the weak convergence rate of an exponential Euler scheme for SDEs governed by coefficients with superlinear growth." Bernoulli 27, no. 1 (2021): 312–47. http://dx.doi.org/10.3150/20-bej1241.

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23

Reisinger, Christoph, and Wolfgang Stockinger. "An adaptive Euler–Maruyama scheme for McKean–Vlasov SDEs with super-linear growth and application to the mean-field FitzHugh–Nagumo model." Journal of Computational and Applied Mathematics 400 (January 2022): 113725. http://dx.doi.org/10.1016/j.cam.2021.113725.

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24

Buckwar, Evelyn, Massimiliano Tamborrino, and Irene Tubikanec. "Spectral density-based and measure-preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs." Statistics and Computing 30, no. 3 (2019): 627–48. http://dx.doi.org/10.1007/s11222-019-09909-6.

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Abstract Approximate Bayesian computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool for modelling time-dependent, real-world phenomena with underlying random effects. When applying ABC to stochastic models, two major difficulties arise: First, the derivation of effective summary statistics and proper distances is particularly challenging, since simulations from the stochastic process under the same parameter configuration result i

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25

Giribone, Pier Giuseppe, and Roberto Revetria. "Certificate pricing using Discrete Event Simulations and System Dynamics theory." Risk Management Magazine 16, no. 2 (2021): 75–93. http://dx.doi.org/10.47473/2020rmm0092.

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The study proposes an innovative application of Discrete Event Simulations (DES) and System Dynamics (SD) theory to the pricing of a certain kind of certificates very popular among private investors and, more generally, in the context of wealth management. The paper shows how numerical simulation software mainly used in traditional engineering, such as industrial and mechanical engineering, can be successfully adapted to the risk analysis of structured financial products. The article can be divided into three macro-sections: in the first part a synthetic overview of the most widespread option

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26

Kadioglu, Samet Y., and Veli Colak. "An Essentially Non-Oscillatory Spectral Deferred Correction Method for Conservation Laws." International Journal of Computational Methods 13, no. 05 (2016): 1650027. http://dx.doi.org/10.1142/s0219876216500274.

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We present a computational method based on the Spectral Deferred Corrections (SDC) time integration technique and the Essentially Non-Oscillatory (ENO) finite volume method for the conservation laws (one-dimensional Euler equations). The SDC technique is used to advance the solutions in time with high-order of accuracy. The ENO method is used to define high-order cell edge quantities that are then used to evaluate numerical fluxes. The coupling of the SDC method with a high-order finite volume method (Piece-wise Parabolic Method (PPM)) for solving the conservation laws is first carried out by

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27

İnce, Nihal, and Aladdin Shamilov. "An Application of New Method to Obtain Probability Density Function of Solution of Stochastic Differential Equations." Applied Mathematics and Nonlinear Sciences 5, no. 1 (2020): 337–48. http://dx.doi.org/10.2478/amns.2020.1.00031.

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AbstractIn this study, a new method to obtain approximate probability density function (pdf) of random variable of solution of stochastic differential equations (SDEs) by using generalized entropy optimization methods (GEOM) is developed. By starting given statistical data and Euler–Maruyama (EM) method approximating SDE are constructed several trajectories of SDEs. The constructed trajectories allow to obtain random variable according to the fixed time. An application of the newly developed method includes SDE model fitting on weekly closing prices of Honda Motor Company stock data between 02

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28

Nabati, Parisa, Hadiseh Babazadeh, and Hamed Azadfar. "Noise analysis of band pass filters using stochastic differential equations." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 38, no. 2 (2019): 693–702. http://dx.doi.org/10.1108/compel-06-2018-0253.

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Purpose The purpose of this paper is to analyze the effects of white noise perturbations of the input voltage on the band pass filter response, both on pass band and reject band. Design/methodology/approach By adding white noise term in the input voltage of the filter circuit, the deterministic ordinary differential equation (ODE) is replaced by a stochastic differential equation (SDE). With the application of Ito lemma, the analytical solution of SDE has been obtained. Furthermore, based on the Euler–Maruyama approximation, the numerical simulation for SDE has been done. Practical implication

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29

Alnafisah, Yousef. "The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method." Abstract and Applied Analysis 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/3805042.

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Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Itô’-Taylor expansion at an appropriate point produces Milstein method for the SDE.

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30

Guyon, Julien. "Euler scheme and tempered distributions." Stochastic Processes and their Applications 116, no. 6 (2006): 877–904. http://dx.doi.org/10.1016/j.spa.2005.11.011.

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31

Golec, Janusz. "Averaging Euler-type difference scheme." Stochastic Analysis and Applications 15, no. 5 (1997): 751–58. http://dx.doi.org/10.1080/07362999708809505.

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32

Dereich, Steffen, and Sangmeng Li. "Multilevel Monte Carlo for Lévy-driven SDEs: Central limit theorems for adaptive Euler schemes." Annals of Applied Probability 26, no. 1 (2016): 136–85. http://dx.doi.org/10.1214/14-aap1087.

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33

Briand, Phillippe, Abir Ghannoum, and Céline Labart. "Mean reflected stochastic differential equations with jumps." Advances in Applied Probability 52, no. 2 (2020): 523–62. http://dx.doi.org/10.1017/apr.2020.11.

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AbstractIn this paper, a reflected stochastic differential equation (SDE) with jumps is studied for the case where the constraint acts on the law of the solution rather than on its paths. These reflected SDEs have been approximated by Briand et al. (2016) using a numerical scheme based on particles systems, when no jumps occur. The main contribution of this paper is to prove the existence and the uniqueness of the solutions to this kind of reflected SDE with jumps and to generalize the results obtained by Briand et al. (2016) to this context.

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34

Böttcher, Björn, and Alexander Schnurr. "The Euler Scheme for Feller Processes." Stochastic Analysis and Applications 29, no. 6 (2011): 1045–56. http://dx.doi.org/10.1080/07362994.2011.610167.

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35

Yan, Liqing. "The Euler scheme with irregular coefficients." Annals of Probability 30, no. 3 (2002): 1172–94. http://dx.doi.org/10.1214/aop/1029867124.

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36

Lin, P., K. W. Morton, and E. Süli. "Euler characteristic Galerkin scheme with recovery." ESAIM: Mathematical Modelling and Numerical Analysis 27, no. 7 (1993): 863–94. http://dx.doi.org/10.1051/m2an/1993270708631.

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37

Pierret, Frédéric. "A non-standard-Euler–Maruyama scheme." Journal of Difference Equations and Applications 22, no. 1 (2015): 75–98. http://dx.doi.org/10.1080/10236198.2015.1076809.

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38

Fan, Yulian. "The PDEs and Numerical Scheme for Derivatives under Uncertainty Volatility." Mathematical Problems in Engineering 2019 (May 29, 2019): 1–7. http://dx.doi.org/10.1155/2019/1268301.

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We use the stochastic differential equations (SDE) driven by G-Brownian motion to describe the basic assets (such as stocks) price processes with volatility uncertainty. We give the estimation method of the SDE’s parameters. Then, by the nonlinear Feynman-Kac formula, we get the partial differential equations satisfied by the derivatives. At last, we give a numerical scheme to solve the nonlinear partial differential equations.

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39

Deepika, Deepika, Ompal Singh, Adarsh Anand, and Jagvinder Singh. "SDE based Unified Scheme for Developing Entropy Prediction Models for OSS." International Journal of Mathematical, Engineering and Management Sciences 6, no. 1 (2020): 207–22. http://dx.doi.org/10.33889/ijmems.2021.6.1.013.

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Today, so as to meet the user's requirement, modification of software is necessarily required. But at the same time, to incorporate these modifications and requirements there are enormous changes which are made to the coding of the software and over a period of time these changes make the software complex. Largely there are three types of code changes occur in the source code namely, bug repair, feature enhancement & addition of new features, but these changes bring the uncertainty in the bug removal rate. In this paper, these uncertainties have been explicitly modeled and using three-dime

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40

Zhao, Weidong, Wei Zhang, and Lili Ju. "A Numerical Method and its Error Estimates for the Decoupled Forward-Backward Stochastic Differential Equations." Communications in Computational Physics 15, no. 3 (2014): 618–46. http://dx.doi.org/10.4208/cicp.280113.190813a.

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AbstractIn this paper, a new numerical method for solving the decoupled forward-backward stochastic differential equations (FBSDEs) is proposed based on some specially derived reference equations. We rigorously analyze errors of the proposed method under general situations. Then we present error estimates for each of the specific cases when some classical numerical schemes for solving the forward SDE are taken in the method; in particular, we prove that the proposed method is second-order accurate if used together with the order-2.0 weak Taylor scheme for the SDE. Some examples are also given

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41

Singh, Manish K., V. Ramesh, and N. Balakrishnan. "Implicit scheme for meshless compressible Euler solver." Engineering Applications of Computational Fluid Mechanics 9, no. 1 (2015): 382–98. http://dx.doi.org/10.1080/19942060.2015.1048621.

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42

Huang, Yenkun, and Che-Yuan Tsai. "Euler Scheme for a Stochastic Goursat Problem." Stochastic Analysis and Applications 22, no. 2 (2004): 275–87. http://dx.doi.org/10.1081/sap-120028590.

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43

Lépingle, D. "Euler scheme for reflected stochastic differential equations." Mathematics and Computers in Simulation 38, no. 1-3 (1995): 119–26. http://dx.doi.org/10.1016/0378-4754(93)e0074-f.

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44

Li, You Guo, and Yuan Fei Dong. "Research on the Forward Euler Difference Method for Parabolic Equations." Advanced Materials Research 998-999 (July 2014): 992–95. http://dx.doi.org/10.4028/www.scientific.net/amr.998-999.992.

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This article is devoted to the forward Euler difference method for the parabolic equation. In this paper, a forward Euler difference scheme is derived. It is shown that the forward Euler difference scheme is convergence and stability. Moreover, a numerical experiment is conducted to illustrate the theoretical results of the presented method.

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45

Mikulevicius, R. "On the rate of convergence of simple and jump-adapted weak Euler schemes for Lévy driven SDEs." Stochastic Processes and their Applications 122, no. 7 (2012): 2730–57. http://dx.doi.org/10.1016/j.spa.2012.04.013.

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46

Zhang, Guo-Dong, and Yinnian He. "Unconditional convergence of the Euler semi-implicit scheme for the 3D incompressible MHD equations." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 8 (2015): 1912–23. http://dx.doi.org/10.1108/hff-08-2014-0257.

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Purpose – The purpose of this paper is to consider the numerical implementation of the Euler semi-implicit scheme for three-dimensional non-stationary magnetohydrodynamics (MHD) equations. The Euler semi-implicit scheme is used for time discretization and (P 1b , P 1, P 1) finite element for velocity, pressure and magnet is used for the spatial discretization. Design/methodology/approach – Several numerical experiments are provided to show this scheme is unconditional stability and unconditional L2−H2 convergence with the L2−H2 optimal error rates for solving the non-stationary MHD flows. Find

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47

Yu-Shun, Wang, Wang Bin, and Chen Xin. "Multisymplectic Euler Box Scheme for the KdV Equation." Chinese Physics Letters 24, no. 2 (2007): 312–14. http://dx.doi.org/10.1088/0256-307x/24/2/003.

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48

Ahn, Hyungsok, and Arturo Kohatsu-Higa. "The euler scheme for anticipating stochastic differential equations." Stochastics and Stochastic Reports 54, no. 3-4 (1995): 247–69. http://dx.doi.org/10.1080/17442509508834008.

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49

Dautov, R. Z., and A. I. Mikheeva. "Implicit Euler scheme for an abstract evolution inequality." Differential Equations 47, no. 8 (2011): 1130–38. http://dx.doi.org/10.1134/s0012266111080076.

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50

Chattot, Jean-Jacques. "A conservative box-scheme for the Euler equations." International Journal for Numerical Methods in Fluids 31, no. 1 (1999): 149–58. http://dx.doi.org/10.1002/(sici)1097-0363(19990915)31:1<149::aid-fld960>3.0.co;2-s.

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