Radchenko V. Integrals with respect to general stochastic measures

The dissertation is devoted to studying of sigma-additive in probability stochastic set functions. The integral of real-valued function with respect to such stochastic measure is considered in detail. For this integral and sequences of integrands, integrators, and sets of integration, limit theorems are obtained. Integral of real-valued functions with respect to sigma-finite stochastic measures is defined and studied. Trajectories of processes generated by values of stochastic measures are considered. Conditions of Besov regularity and continuity of paths are obtained. Parameter stochastic integral with respect to stochastic measures is studied. It is shown that solutions of some classical partial differential equations with random influence may be written in form of integrals with respect to stochastic measures. For random function that is a random series with real functions, symmetric integral with respect to stochastic measure is defined and studied. For two models of asset price derived by Brownian motion and, in addition, having random changes at some jump times, the explicit form of the variance-minimizing hedging strategy is obtained.