Stochastic integrals and stochastic differential equations, which contain fractional Brownian field. (Ukrainian, English) Zbl 1164.60383

Mishura, Yu. S.; Il’chenko, S. A.

Teor. Jmovirn. Mat. Stat. 75, 80-94 (2006); translation in Theory Probab. Math. Stat. 75, 93-108 (2007).

Eestimates are obtained for norms in Besov-type spaces of generalized two-parametric stochastic integrals with respect to a fractional Brownian field on the plane. Then, these estimates are used in the case where the integrand is a functional of a fractional Brownian field on the plane and the integrator is the field itself. A theorem on existence and uniqueness of a solution of a stochastic differential equation with a fractional Brownian field is proved.

Reviewer: Aleksandr D. Borisenko (Kyïv)

MSC:

60H10

Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

stochastic integrals with respect to fractional Brownian field; stochastic differential equations; fractional Brownian field; existence and uniqueness theorem