A Stochastic Reconstruction Theorem on Rectangular Increments with an Application to a Mixed Hyperbolic SPDE

Abstract

We extend the stochastic reconstruction theorem to a setting where the underlying family of distributions satisfies some natural conditions involving rectangular increments. This allows us to prove the well-posedness of a new class of mixed stochastic partial differential of hyperbolic type which combines standard Walsh stochastic integration and Young products.

59 pages, further details on the multi-parameter sewing lemma added