Exponential tightness of a family of Skorohod integrals

TL;DR

This paper investigates the conditions under which a family of Skorohod integrals exhibits exponential tightness, providing counterexamples, characterizations, and applications to clarify its behavior compared to Itô integrals.

Contribution

It introduces new characterizations of exponential tightness for Skorohod integrals and demonstrates that it generally does not hold as it does for Itô integrals, with practical applications.

Findings

Counterexample showing exponential tightness does not hold in general

Characterizations of exponential tightness for Skorohod integrals

Applications illustrating the theoretical results

Abstract

Exponential tightness of a family of Skorohod integrals is studied in this paper. We first provide a counterexample to illustrate that in general the exponential tightness with speed $\epsilon$ similar to It\^o integral does not hold, even for any speed $\epsilon^\alpha$ with $\alpha > 0$. Then, some characterizations of this subject are given. Application is also provided to illustrate the proposed results.