scholarly journals Weak convergence of delay SDEs with applications to Carathéodory approximation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ta Cong Son ◽  
Nguyen Tien Dung ◽  
Nguyen Van Tan ◽  
Tran Manh Cuong ◽  
Hoang Thi Phuong Thao ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Malliavin Calculus ◽  
Time Delays ◽  
Approximation Scheme ◽  
Explicit Estimate ◽  
Fundamental Class

<p style='text-indent:20px;'>In this paper, we consider a fundamental class of stochastic differential equations with time delays. Our aim is to investigate the weak convergence with respect to delay parameter of the solutions. Based on the techniques of Malliavin calculus, we obtain an explicit estimate for the rate of convergence. An application to the Carathéodory approximation scheme of stochastic differential equations is provided as well.</p>

Moderate deviation principle for multivalued stochastic differential equations

2019 ◽  
Vol 20 (03) ◽  
pp. 2050015 ◽  
Author(s):  
Hua Zhang
Keyword(s):  
Brownian Motion ◽  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Moderate Deviation ◽  
Reflected Brownian Motion ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Weak Convergence Approach

In this paper, we prove a moderate deviation principle for the multivalued stochastic differential equations whose proof are based on recently well-developed weak convergence approach. As an application, we obtain the moderate deviation principle for reflected Brownian motion.

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.

A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus

2019 ◽  
Vol 25 (4) ◽  
pp. 341-361
Author(s):  
Riu Naito ◽  
Toshihiro Yamada
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Differential Equations ◽  
Least Squares ◽  
Stochastic Differential Equations ◽  
Malliavin Calculus ◽  
Second Order ◽  
Discretization Method ◽  
Local Approximations ◽  
Backward Sdes

Abstract The paper proposes a new second-order discretization method for forward-backward stochastic differential equations. The method is given by an algorithm with polynomials of Brownian motions where the local approximations using Malliavin calculus play a role. For the implementation, we introduce a new least squares Monte Carlo method for the scheme. A numerical example is illustrated to check the effectiveness.

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