On L_{p}-estimates of some singular integrals related to jump processes

TL;DR

This paper provides estimates for fractional Sobolev and Besov norms of singular integrals associated with jump processes, aiding the analysis of models involving discontinuous signals and observations.

Contribution

It introduces new L_{p}-estimates for singular integrals related to jump processes in the context of the Zakai equation with discontinuities.

Findings

Derived fractional Sobolev norm estimates for singular integrals.

Established bounds for Besov norms in jump process models.

Enhanced understanding of regularity properties in stochastic filtering.

Abstract

We estimate fractional Sobolev and Besov norms of some singular integrals arising in the model problem for the Zakai equation with discontinuous signal and observation.