On solvability of stochastic differential inclusions with current velocities

Abstract

An existence of solution theorem is obtained for stochastic differential inclusions given in terms of the so-called current velocities (direct analogues of ordinary velocity of deterministic systems) and quadratic mean derivatives (giving information on the diffusion coefficient) on the flat n-dimensional torus. The current velocity part is single-valued while the quadratic part is set-valued and takes values in symmetric (2, 0) tensors with unit determinant.

Keywords:

• mean derivatives
• stochastic differential inclusions
• group SL(n)

AMS Subject Classifications::

• 58J65
• 60H10

Acknowledgement

This research is supported in part by RFBR Grant No. 10-01-00143.