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We study stochastic differential equations with Wiener integral considered with respect to fractional Brownian motion with Hurst index H < 1/2. We prove the existence and uniqueness of a strong solution of the equations and find maximal upper bounds for moments of a solution and its increments. We obtain estimates for the distribution of the supremum of a solution on an arbitrary interval. The modulus of continuity of solutions is found and estimates for the distributions of the norms of solutions are obtained in some Lipschitz spaces.

theory of probability and mathematical statistics

Maximal upper bounds for the moments of stochastic integrals and solutions of stochastic differential equations with respect to fractional Brownian motion with Hurst index $H&lt;1/2$. I