On the cross-variation of a class of stochastic processes - Soufiane Moussaten (Results in Applied Mathematics)
The present paper deals with the study of the cross-variation of two-dimensional stochastic process defined using the Young integral with respect to a continuous, α-self-similar Gaussian process that does not necessarily have stationary increments, with increment exponent some β>0. We analyze the limit, in probability, of the so-called cross-variation when β in 0,2α, and we finish by providing some examples of known processes that satisfy the required assumptions.