On a multiple Stratonovich-type integral for some Gaussian processes (Q2433967)

The author constructs a multiple Stratonovich integral with respect to a Gaussian process \(X\) having covariance function of bounded variation on \([0,T]^2\). It is imposed that the integral of a tensor product of functions is the product of the corresponding integrals of order 1. With this definition, it is easy to compute the second order moment of the multiple integral of an elementary function (that is, a finite linear combination of tensor products) by means of Hu-Meyer formula proved for this kind of functions. From this computation, the extension of the integral is obtained by a standard procedure. The integral is then defined on some Banach space of functions.