Speaker:

Alexander Wentzell

Title:

Limit theorems with asymptotic expansions for stochastic processes.

Abstract:

Limit theorems with asymptotic expansions are known for sums of independent random variables. We can try to obtain limit theorems of this kind for families of stochastic processes depending on a parameter. Such theorems can be formulated for expectations of functionals of the trajectories of the stochastic processes, under conditions involving the derivatives of the functionals. Some theorems of this kind are obtained for families of Markov processes with frequent, small jumps.
There is some hope of obtaining asymptotic expansions also for large deviation theorems for families of stochastic processes.

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