Karlikova M. Stochastic flows with interaction

The main object investigated in the thesis is a stochastic differential equation with interaction introduced by A. A. Dorogovtsev. For such an equation new conditions under which weak solution exists are obtained. Markov properties of the solution in spaces of functions C and S are established. For the process in the space C a generator is built on some set of functions and the correspondent martingale problem is shown to have a unique solution. Sufficient conditions of shift-compactness for the measure-valued process corresponding to the equation with interaction, conditions of stability for the measure-valued process and for the stochastic flow are established.