Results 1 to 10 of about 182 (102)

Backward Euler–Maruyama Method for the Random Periodic Solution of a Stochastic Differential Equation with a Monotone Drift [PDF]

Journal of Theoretical Probability, 2022
AbstractIn this paper, we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler–Maruyama method.
Yue Wu, Yue Wu
openaire   +6 more sources

Error estimates of the backward Euler–Maruyama method for multi-valued stochastic differential equations [PDF]

BIT Numerical Mathematics, 2021
AbstractIn this paper we derive error estimates of the backward Euler–Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is not continuously differentiable but assumed to be convex. We show that the backward Euler–Maruyama method is
Monika Eisenmann, Mihály Kovács, Raphael Kruse, Stig Larsson   +3 more
openaire   +5 more sources

The backward Euler-Maruyama method for invariant measures of stochastic differential equations with super-linear coefficients

Applied Numerical Mathematics, 2023
The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and uniqueness of the invariant measure of the numerical solution generated by the BEM method are proved and the convergence ...
Liu, Wei, Mao, Xuerong, Wu, Yue
openaire   +6 more sources

Analysis of stability for stochastic delay integro-differential equations [PDF]

Journal of Inequalities and Applications, 2018
In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step ...
Yu Zhang, Longsuo Li
doaj   +2 more sources

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, Yasser Taherinasab, Mohammad Amini   +2 more
doaj   +1 more source

Almost Sure Exponential Stability of Numerical Solutions for Stochastic Pantograph Differential Equations with Poisson Jumps

Mathematics, 2022
The stability analysis of the numerical solutions of stochastic models has gained great interest, but there is not much research about the stability of stochastic pantograph differential equations.
Amr Abou-Senna, Boping Tian
doaj   +1 more source

Existence, uniqueness and stability of solutions to fractional backward stochastic differential equations

Applied Mathematics in Science and Engineering, 2022
Many types of fractional stochastic differential equation (FrSDE), such as Caputo, fractional Brown motion derivatives, and Mittag-Later functions, exist.
Jiahao Chen, Suoao Ke, Xiaofei Li, Wenbo Liu   +3 more
doaj   +1 more source

Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients [PDF]

Stochastics, 2012
In this work, we generalize the current theory of strong convergence rates for the backward Euler–Maruyama scheme for highly non-linear stochastic differential equations, which appear in both mathematical finance and bio-mathematics. More precisely, we show that under a dissipative condition on the drift coefficient and superlinear growth condition on ...
Mao, Xuerong, Szpruch, Lukasz
openaire   +3 more sources

Almost Surely Exponential Stability of Numerical Solutions for Stochastic Pantograph Equations

Abstract and Applied Analysis, 2014
Our effort is to develop a criterion on almost surely exponential stability of numerical solution to stochastic pantograph differential equations, with the help of the discrete semimartingale convergence theorem and the technique used in stable analysis ...
Shaobo Zhou
doaj   +1 more source

The backward Euler-Maruyama method for invariant measures of stochastic differential equations with super-linear coefficients [PDF]

, 2022
The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and uniqueness of the invariant measure of the numerical solution generated by the BEM method are proved and the convergence ...
Liu, Wei, Mao, Xuerong, Wu, Yue
openaire