Abstract
We obtain sufficient conditions for nonoccurrence of explosion for solutions of one-dimensional stochastic differential equation (SDE) driven by fractional Brownian motion (fBm) with Hurst parameter H ∈ (1/2, 1); SDE is interpreted as a stochastic integral equation of the fractional Ito-integral type. In the case where explosion cannot occur, every solution of SDE exists in the future. One of our result corresponds to an extension of the Wintner theorem on continuation of solutions of ordinary differential equations. We shall obtain a priori bounds for nonexplosive solution and also give an example of explosive solutions.
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