Explosion and asymptotic behavior of nonlinear Itô type stochastic integrodifferential equations. (English) Zbl 0594.60061
The paper deals with the study of explosion and growth order of solution of a general class of Itô-type stochastic differential equations
\[
dx(t)=F(t,x(t),\int^{t}_{t_ 0}f_ 1(t,s,x(s))ds,\int^{t}_{t_ 0}f_ 2(t,\quad s,x(s))dW_ s)dt+
\]
\[ +H(t,x(t),\int^{t}_{t_ 0}h_ 1(t,s,x(s))ds,\int^{t}_{t_ 0}h_ 2(t,s,x(s\quad))dW_ s)dW_ t \] where \(\{W_ t\}\) is a Brownian motion process. Sufficient conditions for infinite explosion time and asymptotic behavior of solutions are investigated.
\[ +H(t,x(t),\int^{t}_{t_ 0}h_ 1(t,s,x(s))ds,\int^{t}_{t_ 0}h_ 2(t,s,x(s\quad))dW_ s)dW_ t \] where \(\{W_ t\}\) is a Brownian motion process. Sufficient conditions for infinite explosion time and asymptotic behavior of solutions are investigated.
Reviewer: D.Jaruskova
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H20 | Stochastic integral equations |
Keywords:
explosion and growth order; Sufficient conditions for infinite explosion time; asymptotic behavior of solutionsReferences:
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