Asymptotic behavior of the martingale type integral functionals for unstable solutions to stochastic differential equations

2015 ◽  
Vol 90 ◽  
pp. 115-126 ◽  
Author(s):  
G. L. Kulinich ◽  
S. V. Kushnirenko ◽  
Yu. S. Mishura
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Integral Functionals ◽  
Type Integral ◽  
Unstable Solutions

Lyapunov Type Integral Inequalities for Certain Differential Equations

1997 ◽  
Vol 4 (2) ◽  
pp. 139-148
Author(s):  
B. G. Pachpatte
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Second Order ◽  
Integral Inequalities ◽  
Asymptotic Behavior Of Solutions ◽  
Second Order Differential Equations ◽  
Elementary Analysis ◽  
Type Integral ◽  
Zeros Of Solutions

Abstract In the present paper we establish Lyapunov type integral inequalities related to the zeros of solutions of certain second-order differential equations by using elementary analysis. We also present some immediate applications of our results to study the asymptotic behavior of solutions of the corresponding differential equations.

scholarly journals Asymptotic properties of coupled forward–backward stochastic differential equations

2014 ◽  
Vol 14 (03) ◽  
pp. 1450004 ◽  
Author(s):  
Ana Bela Cruzeiro ◽  
André de Oliveira Gomes ◽  
Liangquan Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Asymptotic Properties ◽  
Backward Stochastic Differential Equations ◽  
Type Formula ◽  
Deviation Principle

In this paper, we consider coupled forward–backward stochastic differential equations (FBSDEs in short) with parameter ε > 0, of the following type [Formula: see text] We study the asymptotic behavior of its solutions and establish a large deviation principle for the corresponding processes.

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