Strong Convergence of the Split-Step Theta Method for Stochastic Delay Differential Equations with Nonglobally Lipschitz Continuous Coefficients [PDF]
Abstract and Applied Analysis, 2014 This paper is concerned with the convergence analysis of numerical methods for stochastic delay differential equations. We consider the split-step theta method for nonlinear nonautonomous equations and prove the strong convergence of the numerical ...
Chao Yue, Chengming Huang
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Double barrier reflected BSDEs with stochastic Lipschitz coefficient [PDF]
Modern Stochastics: Theory and Applications, 2017 This paper proves the existence and uniqueness of a solution to doubly reflected backward stochastic differential equations where the coefficient is stochastic Lipschitz, by means of the penalization method.
Mohamed Marzougue, Mohamed El Otmani
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Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient
Mathematics, 2020 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.
Kęstutis Kubilius, Aidas Medžiūnas
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The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate [PDF]
Advances in Difference Equations, 2019 The Euler scheme is one of the standard schemes to obtain numerical approximations of solutions of stochastic differential equations (SDEs). Its convergence properties are well known in the case of globally Lipschitz continuous coefficients.
S. Göttlich, K. Lux, A. Neuenkirch
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Stochastic Analysis and ApplicationsWe consider an infinite horizon, obliquely reflected backward stochastic differential equation (RBSDE). The main contribution of the present work is that we generalize previous results on infinite horizon RBSDEs to the setting where the driver has a ...
Perninge, Magnus,, Perninge, Magnus
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Exponential ergodicity of non-Lipschitz multivalued stochastic differential equations
Bulletin Des Sciences Mathematiques, 2010 Under the conditions of coefficients being non-Lipschitz and the diffusion coefficient being elliptic, we study the strong Feller property and irreducibility for the transition probability of solutions to general multivalued stochastic differential ...
Jiagang Ren, X -C Zhang
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MathematicsIn this paper, we focus on mean-field stochastic differential equations driven by G-Brownian motion (G-MFSDEs for short) with a drift coefficient satisfying the local one-sided Lipschitz condition with respect to the state variable and the global ...
Pengfei Zhao, Haiyan Yuan
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Backward Euler method for stochastic differential equations with non-Lipschitz coefficients
CoRR, 2022 We study the traditional backward Euler method for $m$-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H > 1/2$ whose drift coefficient satisfies the one-sided Lipschitz condition.
Zhou, Hao, Hu, Yaozhong, Liu, Yanghui
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Modified Runge–Kutta method with convergence analysis for nonlinear stochastic differential equations with Hölder continuous diffusion coefficient [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2023 The main goal of this work is to develop and analyze an accurate trun-cated stochastic Runge–Kutta (TSRK2) method to obtain strong numeri-cal solutions of nonlinear one-dimensional stochastic differential equations (SDEs) with continuous Hölder diffusion
A. Haghighi
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Mean-square stability and convergence of compensated split-step θ-method for nonlinear jump diffusion systems [PDF]
Mathematics and Modeling in Finance, 2021 In this paper, the existence and uniqueness of the numerical solution of the Stochastic Differential Equations with Jumps(SDEwJs) under the one side Lipschitz conditions and polynomial growth conditions are presented.
Ali Soheili +2 more
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