Explosion and asymptotic behavior of nonlinear Itô type stochastic integrodifferential equations (Q1077085)

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.