Electron. J. Diff. Equ., Vol. 2016 (2016), No. 194, pp. 1-14.

Theorems on boundedness of solutions to stochastic delay differential equations

Youssef N. Raffoul, Dan Ren

Abstract:
In this report, we provide general theorems about boundedness or bounded in probability of solutions to nonlinear delay stochastic differential systems. Our analysis is based on the successful construction of suitable Lyapunov functionals. We offer several examples as application of our theorems.

Submitted March 18, 2016. Published July 18, 2016.
Math Subject Classifications: 34F05, 60H10, 65Q10.
Key Words: Stochastically bounded; bounded in probability; Lyapunov functional; inequalities; stochastic Volterra integro-differential system.

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Youssef N. Raffoul
Department of Mathematics
University of Dayton
Dayton, OH 45469-2316, USA
email: yraffoul1@udayton.edu
  Dan Ren
Department of Mathematics
University of Dayton
Dayton, OH 45469-2316, USA
email: dren01@udayton.edu

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