In this article, we construct a Stratonovich solution for the stochastic wave equation in spatial dimension $$d \le 2$$ , with time-independent noise and linear term $$\sigma (u)=u$$ multiplying noise. The is spatially homogeneous its spectral measure satisfies an integrability condition which stronger than Dalang’s condition. We give probabilistic representation solution, similar to Feynman–Ka...

We recall the successes of the Hubbard-Stratonovich Transformation (HST) of many-body theory, point out its failure to cope with competing channels of collective phenomena and show how to overcome this by Variational Perturbation Theory. That yields exponentially fast converging results, thanks to the help of a variety of collective classical fields, rather than a fluctuating collective quantum...

Suppose that X1, . . . , Xn are continuous semimartingales that are reversible and have nondegenerate crossings. Then the corresponding rank processes can be represented by generalized Stratonovich integrals, and this representation can be used to decompose the relative log-return of portfolios generated by functions of ranked market weights. Introduction For n ≥ 2, consider a family of continu...