scholarly journals High-order split-step theta methods for non-autonomous stochastic differential equations with non-globally Lipschitz continuous coefficients

2016 ◽  
Vol 39 (9) ◽  
pp. 2380-2400 ◽  
Author(s):  
Chao Yue
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
High Order ◽  
Lipschitz Continuous

scholarly journals Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds

2021 ◽  
Author(s):  
Adrien Laurent ◽  
Gilles Vilmart
Keyword(s):  
Invariant Measure ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Linear Group ◽  
Langevin Equation ◽  
Numerical Experiments ◽  
Special Linear Group ◽  
Order Conditions ◽  
High Order ◽  
Differential Equations On Manifolds

AbstractWe derive a new methodology for the construction of high-order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold. We obtain the order conditions for sampling the invariant measure for a class of Runge–Kutta methods applied to the constrained overdamped Langevin equation. The analysis is valid for arbitrarily high order and relies on an extension of the exotic aromatic Butcher-series formalism. To illustrate the methodology, a method of order two is introduced, and numerical experiments on the sphere, the torus and the special linear group confirm the theoretical findings.

L2-regularity result for solutions of backward doubly stochastic differential equations

2019 ◽  
Vol 20 (02) ◽  
pp. 2050012
Author(s):  
Achref Bachouch ◽  
Anis Matoussi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Numerical Scheme ◽  
Regularity Result ◽  
Time Discretization ◽  
Lipschitz Continuous ◽  
Doubly Stochastic

We prove an [Formula: see text]-regularity result for the solutions of Forward Backward doubly stochastic differential equations (F-BDSDEs) under globally Lipschitz continuous assumptions on the coefficients. As an application of our result, we derive the rate of convergence in time for the (Euler time discretization-based) numerical scheme for F-BDSDEs proposed by Bachouch et al. (2016) under only globally Lipschitz continuous assumptions.

Comparison Theorem for any Solutions of Backward Stochastic Differential Equations and its Application

2012 ◽  
Vol 524-527 ◽  
pp. 3801-3804
Author(s):  
Shi Yu Li ◽  
Wu Jun Gao ◽  
Jin Hui Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Equations ◽  
Local Martingale ◽  
One Dimensional ◽  
Lipschitz Continuous ◽  
The One ◽  
Uniformly Lipschitz

ƒIn this paper, we study the one-dimensional backward stochastic equations driven by continuous local martingale. We establish a generalized the comparison theorem for any solutions where the coefficient is uniformly Lipschitz continuous in z and is equi-continuous in y.

High order weak approximation for irregular functionals of time-inhomogeneous SDEs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Toshihiro Yamada
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Approximation Method ◽  
Numerical Experiments ◽  
Higher Order ◽  
High Order ◽  
Weak Approximation ◽  
Discretization Scheme ◽  
Unified Approach

Abstract This paper shows a general weak approximation method for time-inhomogeneous stochastic differential equations (SDEs) using Malliavin weights. A unified approach is introduced to construct a higher order discretization scheme for expectations of non-smooth functionals of solutions of time-inhomogeneous SDEs. Numerical experiments show the validity of the method.

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