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Approximation properties for solutions to non‐Lipschitz stochastic differential equations with Lévy noise
Author(s) -
Xu Yong,
Pei Bin,
Li Yongge
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3208
Subject(s) - lipschitz continuity , mathematics , stochastic differential equation , stochastic partial differential equation , mathematical analysis , noise (video) , differential equation , lipschitz domain , computer science , artificial intelligence , image (mathematics)
In this paper, we consider the non‐Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Lévy noise, and the approximation theorems for the solutions to these two kinds of equations will be proposed respectively. Non‐Lipschitz condition is much weaker condition than the Lipschitz one. The simplified equations will be defined to make its solutions converge to that of the corresponding original equations both in the sense of mean square and probability, which constitute the approximation theorems. Copyright © 2014 John Wiley & Sons, Ltd.