The integral inequality and applications to stability theorems of stochastic differential equations with respect to semimartingales

1994 ◽  
Vol 46 (3-4) ◽  
pp. 269-281
Author(s):  
Takeshi Taniguchi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Integral Inequality ◽  
Stability Theorems

scholarly journals Existence and Ulam-Hyers-Rassias stability of stochastic differential equations with random impulses

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 399-407
Author(s):  
Wenxuan Lang ◽  
Sufang Deng ◽  
Xiao-Bao Shu ◽  
Fei Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Point Theorem ◽  
Integral Inequality ◽  
Existence Of Solutions ◽  
Stability Of Solutions ◽  
Random Impulses ◽  
Rassias Stability

In this paper, we investigate the existence and Ulam-Hyers-Rassias stability of solutions for stochastic differential equations with random impulses. Based on the Krasnoselskii?s fixed point theorem, we perform investigations on the existence of solutions to the system of stochastic differential equations with random impulses. We apply the integral inequality of Gronwall type to the equations and study their Ulam-Hyers-Rassias stability.

Stochastic Differential Equations for Power Law Behaviors

2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Power Law

scholarly journals Strong Solution Existence for a Class of Degenerate Stochastic Differential Equations

2020 ◽  
Vol 53 (2) ◽  
pp. 2220-2224
Author(s):  
William M. McEneaney ◽  
Hidehiro Kaise ◽  
Peter M. Dower ◽  
Ruobing Zhao
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Strong Solution ◽  
Solution Existence
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