Higher-order stochastic differential equations and the positive Wigner function

2017 ◽  
Vol 96 (6) ◽  
Author(s):  
P. D. Drummond
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Wigner Function ◽  
Higher Order

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.

scholarly journals Well posedness results for higher-order neutral stochastic differential equations driven by Poisson jumps and Rosenblatt process

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 353-365
Author(s):  
K. Ramkumar ◽  
K. Ravikumar ◽  
A. Anguraj ◽  
Hamdy Ahmed
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Successive Approximation Method ◽  
Poisson Jumps ◽  
Rosenblatt Process

In this article, we investigate the existence, uniqueness and stability of mild solutions for a class of higher-order nonautonomous neutral stochastic differential equations (NSDEs) with infinite delay driven by Poisson jumps and Rosenblatt process in Hilbert space. More precisely, using semigroup theory and successive approximation method, we establish a set of sufficient conditions for obtained the required result. Further, the result is deduced to study the higher-order autonomous system. Finally, examples are provided to demonstrate the obtain results.

Implicit Order 3/2 Strong Method for Numerical Solutions of Stratonovich Stochastic Differential Equations

2019 ◽  
Vol 16 (8) ◽  
pp. 3137-3140
Author(s):  
Yazid Alhojilan
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Approximation Method ◽  
Taylor Expansion ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Higher Order ◽  
Implicit Method ◽  
Kutta Method ◽  
Runge Kutta Method

Due to that the explicit methods in solving stochastic differential equations give instability and inaccurate results, the aim of this paper is to derive an effective implicit method gives higher-order approximate solutions for a stiff stochastic differential equations by using Runge-Kutta method. It relies on the Stratonovich-Taylor expansion and uses the notion of perturbation and coupling to carry out the method. The validity of this new approximation method is shown by implementing in MATLAB and, showing the convergence of the method graphically.

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