Maximal type inequalities for linear stochastic Volterra equations

TL;DR

This paper establishes maximal inequalities and tail estimates for solutions of linear stochastic Volterra equations using fractional stochastic calculus, extending previous semigroup-based results to non-semigroup cases.

Contribution

It introduces new maximal inequalities and tail bounds for stochastic Volterra equations without relying on semigroup properties.

Findings

Proved two maximal inequalities for stochastic Volterra equations.

Derived exponential tail estimates for solutions.

Extended results from semigroup to non-semigroup cases.

Abstract

The note is devoted to estimates for convolutions appearing in some class of stochastic Volterra equations. Two maximal inequalities and exponential tail estimate are proved by the fractional method of infinite dimensional stochastic calculus. The paper extends on non-semigroup case some results obtained earlier for semigroups.