scholarly journals An Averaging Principle for Caputo Fractional Stochastic Differential Equations with Compensated Poisson Random Measure

2022 ◽  
Vol 35 (1) ◽  
pp. 1-10
Author(s):  
Zhongkai Guo
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Random Measure ◽  
Averaging Principle ◽  
Poisson Random Measure ◽  
Fractional Stochastic Differential Equations ◽  
Compensated Poisson Random Measure

Prediction-Correction Scheme for Decoupled Forward Backward Stochastic Differential Equations with Jumps

2016 ◽  
Vol 6 (3) ◽  
pp. 253-277 ◽  
Author(s):  
Yu Fu ◽  
Jie Yang ◽  
Weidong Zhao
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Random Measure ◽  
Backward Stochastic Differential Equations ◽  
Explicit Scheme ◽  
Poisson Random Measure ◽  
Correction Scheme ◽  
Compensated Poisson Random Measure ◽  
Theoretical Results ◽  
General Error

AbstractBy introducing a new Gaussian process and a new compensated Poisson random measure, we propose an explicit prediction-correction scheme for solving decoupled forward backward stochastic differential equations with jumps (FBSDEJs). For this scheme, we first theoretically obtain a general error estimate result, which implies that the scheme is stable. Then using this result, we rigorously prove that the accuracy of the explicit scheme can be of second order. Finally, we carry out some numerical experiments to verify our theoretical results.

scholarly journals An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Weifeng Wang ◽  
Lei Yan ◽  
Junhao Hu ◽  
Zhongkai Guo
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Averaging Principle ◽  
Convergence Results ◽  
Fractional Stochastic Differential Equations

In this paper, we want to establish an averaging principle for Mckean–Vlasov-type Caputo fractional stochastic differential equations with Brownian motion. Compared with the classic averaging condition for stochastic differential equation, we propose a new averaging condition and obtain the averaging convergence results for Mckean–Vlasov-type Caputo fractional stochastic differential equations.

An averaging principle for stochastic differential equations of fractional order 0 < α < 1

2020 ◽  
Vol 23 (3) ◽  
pp. 908-919 ◽  
Author(s):  
Wenjing Xu ◽  
Wei Xu ◽  
Kai Lu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Order ◽  
Mild Solution ◽  
Averaging Principle ◽  
Mean Square ◽  
Fractional Systems ◽  
Before And After ◽  
Fractional Stochastic Differential Equations ◽  
Fractional Equation

AbstractThis paper presents an averaging principle for fractional stochastic differential equations in ℝn with fractional order 0 < α < 1. We obtain a time-averaged equation under suitable conditions, such that the solutions to original fractional equation can be approximated by solutions to simpler averaged equation. By mathematical manipulations, we show that the mild solution of two equations before and after averaging are equivalent in the sense of mean square, which means the classical Khasminskii approach for the integer order systems can be extended to fractional systems.

scholarly journals Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hui Yu ◽  
Minghui Song
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Linear Growth ◽  
Numerical Solutions ◽  
Random Measure ◽  
Euler Method ◽  
Poisson Random Measure ◽  
Euler’S Method ◽  
Linear Growth Condition

The numerical methods in the current known literature require the stochastic differential equations (SDEs) driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler's method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. The main aim is to investigate the convergence of the Euler method in probability to such equations with non-Lipschitz coefficients. Numerical example is given to demonstrate our results.

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