Tantsiura M. Limit theorems for countable systems of stochastic differential equations with interaction

The thesis is devoted to infinite systems of stochastic differential equations and the limit behavior of solutions of such systems. Theorems are proved on existence of a weak solution and on existence and uniqueness of a strong solution of infinite systems of stochastic differential equations with non-Lipschitz coefficients. Theorems are proved on existence of a weak solution and on existence and uniqueness of a strong solution of the analogue of the McKean-Vlasov equation for the case when the mass distibution of the particles is a locally finite measure. It is proved that solution of such equation is a limit of a sequence of solutions of infinite systems of stochastic differential equations such that the mass of each particle tends to zero, and the density of particles grows to infinity.