Malovichko T. Properties of stochastic flows correspondent to equations with interaction

The thesis is devoted to study of properties of stochastic flowsith a difficult structure, namely of stochastic flows сorrespondent to equations with interaction and stochastic flows with coalescence. Properties of the Wiener process with variable phase space are studied. The behaviour of the semigroup of the Wiener process with coalescence in two dimensions is studied. The weak convergency of n-point motions of flows of solutions of stochastic differential equations with interaction to n-point motion of the Arratia flow is proved. We construct a diffusion process with coalescence and a diffusion flow with coalescence. Analogues of the Girsanov theorem for stochastic flows with coalescence and for flows of solutions of a class of stochastic differential are proved.