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

TL;DR

This paper extends a stochastic reconstruction theorem to handle rectangular increments, enabling the proof of well-posedness for a new class of mixed hyperbolic SPDEs combining Walsh stochastic integration and Young products.

Contribution

It introduces an extended stochastic reconstruction theorem for rectangular increments and applies it to establish well-posedness of novel mixed hyperbolic SPDEs.

Findings

Extended stochastic reconstruction theorem for rectangular increments

Proved well-posedness of a new class of mixed hyperbolic SPDEs

Combined Walsh stochastic integration with Young products

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.