Efficient Simulation of Stochastic Differential Equations Based on Markov Chain Approximations With Applications

2020 ◽  
Author(s):  
Zhenyu Cui ◽  
Justin Kirkby ◽  
Duy Nguyen
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Efficient Simulation ◽  
Markov Chain Approximations

scholarly journals Multi-valued backward stochastic differential equations with regime switching

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ruijuan Deng ◽  
Yong Ren
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Regime Switching ◽  
Original System ◽  
Backward Stochastic Differential Equations ◽  
Lower Semi ◽  
Finite State ◽  
Uniqueness Of The Solution ◽  
Continuous Convex Function

AbstractThe paper considers a class of multi-valued backward stochastic differential equations with subdifferential of a lower semi-continuous convex function with regime switching, whose generator is a continuous-time Markov chain with a finite state space. Firstly, we get the existence and uniqueness of the solution by the penalization method. Secondly, we prove that the solution of the original system is weakly convergent. Finally, we give an application to the homogenization of a class of multi-valued PDEs with Markov chain.

On solving stochastic differential equations

2019 ◽  
Vol 25 (2) ◽  
pp. 155-161
Author(s):  
Sergej M. Ermakov ◽  
Anna A. Pogosian
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Integral Equations ◽  
Wide Class ◽  
Monte Carlo Methods ◽  
New Approach ◽  
Difference Approximations

Abstract This paper proposes a new approach to solving Ito stochastic differential equations. It is based on the well-known Monte Carlo methods for solving integral equations (Neumann–Ulam scheme, Markov chain Monte Carlo). The estimates of the solution for a wide class of equations do not have a bias, which distinguishes them from estimates based on difference approximations (Euler, Milstein methods, etc.).

scholarly journals The truncated Milstein method for super-linear stochastic differential equations with Markovian switching

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Weijun Zhan ◽  
Qian Guo ◽  
Yuhao Cong
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Convergence Rate ◽  
Stochastic Differential Equations ◽  
Convergence Result ◽  
Convergence Order ◽  
Mean Square ◽  
Numerical Example ◽  
Milstein Method ◽  
The Mean

<p style='text-indent:20px;'>In this paper, to approximate the super-linear stochastic differential equations modulated by a Markov chain, we investigate a truncated Milstein method with convergence order 1 in the mean-square sense. Under Khasminskii-type conditions, we establish the convergence result by employing a relationship between local and global errors. Finally, we confirm the convergence rate by a numerical example.</p>

scholarly journals Dynamics of Markov chains and stable manifolds for random diffeomorphisms

1987 ◽  
Vol 7 (3) ◽  
pp. 351-374 ◽  
Author(s):  
M. Brin ◽  
Yu. Kifer
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Markov Chains ◽  
Stochastic Differential Equations ◽  
Compact Manifold ◽  
Diffusion Processes ◽  
Global Dynamics ◽  
Continuous Transition ◽  
Common Distribution ◽  
Transition Densities

AbstractWe consider the Markov chain on a compact manifold M generated by a sequence of random diffeomorphisms, i.e. a sequence of independent Diff2(M)-valued random variables with common distribution. Random diffeomorphisms appear for instance when diffusion processes are considered as solutions of stochastic differential equations. We discuss the global dynamics of Markov chains with continuous transition densities and construct non-random stable foliations for random diffeomorphisms.

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