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We study sufficient conditions for the weak convergence of stochastic integrals with respect to processes of bounded variation, martingales, or semimartingales. A semimartingale theorem is extended to the multidimensional case. We apply a limit procedure and pass from processes of bounded variation to risk processes. An “inverse” problem for the weak convergence is also considered.

theory of probability and mathematical statistics

Functional limit theorems for stochastic integrals with applications to risk processes and to self-financing strategies in a multidimensional market. I