scholarly journals Convergence and stability of implicit compensated Euler method for stochastic differential equations with Poisson random measure

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Minghui Song ◽  
Hui Yu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Random Measure ◽  
Euler Method ◽  
Poisson Random Measure ◽  
Convergence And Stability

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.

Predictable solution for reflected BSDEs when the obstacle is not right-continuous

2020 ◽  
Vol 28 (4) ◽  
pp. 269-279
Author(s):  
Mohamed Marzougue ◽  
Mohamed El Otmani
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Random Measure ◽  
Backward Stochastic Differential Equations ◽  
Poisson Random Measure ◽  
One Dimensional ◽  
General Filtration ◽  
Reflected Bsdes

AbstractIn the present paper, we consider reflected backward stochastic differential equations when the reflecting obstacle is not necessarily right-continuous in a general filtration that supports a one-dimensional Brownian motion and an independent Poisson random measure. We prove the existence and uniqueness of a predictable solution for such equations under the stochastic Lipschitz coefficient by using the predictable Mertens decomposition.

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.

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