Pathwise stochastic integrals and It\^o formula for multidimensional Gaussian processes

In this article we study existence of pathwise stochastic integrals with respect to a general class of $n$-dimensional Gaussian processes and a wide class of adapted integrands. More precisely, we study integrands which are functions that are of locally bounded variation with respect to all variables. Moreover, multidimensional It\^o formula is derived.