scholarly journals A higher order weak approximation scheme of multidimensional stochastic differential equations using Malliavin weights

2017 ◽  
Vol 321 ◽  
pp. 427-447 ◽  
Author(s):  
Toshihiro Yamada
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Approximation Scheme ◽  
Higher Order ◽  
Weak Approximation

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.

A third-order weak approximation of multidimensional Itô stochastic differential equations

2019 ◽  
Vol 25 (2) ◽  
pp. 97-120 ◽  
Author(s):  
Riu Naito ◽  
Toshihiro Yamada
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Wiener Space ◽  
Weak Approximation ◽  
Third Order ◽  
Brownian Motions ◽  
Numerical Examples ◽  
Discretization Algorithm

Abstract This paper proposes a new third-order discretization algorithm for multidimensional Itô stochastic differential equations driven by Brownian motions. The scheme is constructed by the Euler–Maruyama scheme with a stochastic weight given by polynomials of Brownian motions, which is simply implemented by a Monte Carlo method. The method of Watanabe distributions on Wiener space is effectively applied in the computation of the polynomial weight of Brownian motions. Numerical examples are shown to confirm the accuracy of the scheme.

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