scholarly journals Numerical Simulations of Stochastic Differential Equations with Multiple Conserved Quantities by Conservative Methods

2022 ◽  
Vol 12 (1) ◽  
pp. 53-71
Author(s):  
Zhenyu Wang
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Conserved Quantities

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.

scholarly journals Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Huili Xiang ◽  
Zhuang Fang ◽  
Zuxiong Li ◽  
Zhijun Liu
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Environmental Noise ◽  
Competitive System ◽  
Stochastic Boundedness

A competitive system subject to environmental noise is established. By using the theory of stochastic differential equations and Lyapunov function, sufficient conditions for the existence, uniqueness, stochastic boundedness, and global attraction of the positive solution of the above system are established, respectively. An example together with its corresponding numerical simulations is presented to confirm our analytical results.

scholarly journals Projection methods for stochastic differential equations with conserved quantities

2016 ◽  
Vol 56 (4) ◽  
pp. 1497-1518 ◽  
Author(s):  
Weien Zhou ◽  
Liying Zhang ◽  
Jialin Hong ◽  
Songhe Song
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Projection Methods ◽  
Conserved Quantities

scholarly journals Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2195
Author(s):  
Zhenyu Wang ◽  
Qiang Ma ◽  
Xiaohua Ding
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Computational Cost ◽  
Conserved Quantity ◽  
Conserved Quantities ◽  
Mean Square Convergence ◽  
The Mean ◽  
Runge Kutta ◽  
Improved Methods ◽  
Theoretical Results

Explicit numerical methods have a great advantage in computational cost, but they usually fail to preserve the conserved quantity of original stochastic differential equations (SDEs). In order to overcome this problem, two improved versions of explicit stochastic Runge–Kutta methods are given such that the improved methods can preserve conserved quantity of the original SDEs in Stratonovich sense. In addition, in order to deal with SDEs with multiple conserved quantities, a strategy is represented so that the improved methods can preserve multiple conserved quantities. The mean-square convergence and ability to preserve conserved quantity of the proposed methods are proved. Numerical experiments are implemented to support the theoretical results.

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