Convergence Rates for Adaptive Weak Approximation of Stochastic Differential Equations

2005 ◽  
Vol 23 (3) ◽  
pp. 511-558 ◽  
Author(s):  
Kyoung-Sook Moon ◽  
Anders Szepessy ◽  
Raúl Tempone ◽  
Georgios E. Zouraris
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Convergence Rates ◽  
Weak Approximation

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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