Numerical simulations for stochastic differential equations on manifolds by stochastic symmetric projection method

2020 ◽  
Vol 541 ◽  
pp. 123305
Author(s):  
Zhenyu Wang ◽  
Chenke Wang ◽  
Qiang Ma ◽  
Xiaohua Ding
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Projection Method ◽  
Differential Equations On Manifolds

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.

scholarly journals The stochastic θ method for stationary distribution of stochastic differential equations with Markovian switching

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yanan Jiang ◽  
Liangjian Hu ◽  
Jianqiu Lu
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Stationary Distribution ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Markovian Switching ◽  
Theoretical Results

AbstractIn this paper, stationary distribution of stochastic differential equations (SDEs) with Markovian switching is approximated by numerical solutions generated by the stochastic θ method. We prove the existence and uniqueness of stationary distribution of the numerical solutions firstly. Then, the convergence of numerical stationary distribution to the underlying one is discussed. Numerical simulations are conducted to support the theoretical results.

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