Stochastic differential equations of second order with a small parameter

Abstract

We consider boundary value problems for stochastic differential equations of second order with a small parameter. For this case we prove a special existence and unicity theorem for strong solutions. The asymptotic behavior of these solutions as small parameter goes to zero is studied. The stochastic averaging theorem for such equations is shown. The limits in the explicit form for the solutions as a small parameter goes to zero are found.

The research is partually funded by the grant of the Government of Russian Federation $n^{\circ }$14.A12.31.0007 and by The National Research Tomsk State University Academic D.I. Mendeleev Fund Program (NU 8.1.55.2015 L) in 2014- 2015