Stochastic Integration Based on Simple, Symmetric Random Walks

A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method is didactically more advantageous, more transparent, and technically less demanding than other existing ones. In a large part of the theory one has a.s. uniform convergence on compacts. In particular, the method gives a.s. convergence for the stochastic integral of a finite variation function of the integrator, which is not càdlàg in general. Research of T. Szabados was supported by a Hungarian National Research Foundation (OTKA) grant No. T42496. Research of B. Székely was supported by the HSN laboratory of BUTE.