On the convergence of stochastic integrals with respect to \(p\)-semimartingales (Q951213)

The paper considers a new class of processes which is wider than the semimartingale class and contains the fractional Brownian motion. This new class is denoted as the class of \(p\)-semimartingales and it is constructed as the set of processes that can be written as the sum of a bounded \(p\)-variation process and a martingale. The sufficient conditions for the weal convergence of stochastic integrals with respect to \(p\)-semimartingales has been obtained. These conditions can be simplified if the integrating process is pathwise constant.