Stochastic differential equations driven by generalized grey noise

TL;DR

This paper develops a substitution formula for stochastic differential equations driven by generalized grey noise, enabling analysis of solution properties like absolute continuity, positivity, and smoothness of the density.

Contribution

The paper introduces a novel substitution formula for SDEs driven by generalized grey noise, advancing understanding of their solution distributions.

Findings

Established absolute continuity of solutions

Proved positivity of the solution density

Derived upper bounds and smoothness of the density

Abstract

In this paper we establish a substitution formula for stochastic differential equation driven by generalized grey noise. We then apply this formula to investigate the absolute continuity of the solution with respect to the Lebesgue measure and the positivity of the density. Finally, we derive an upper bound and show the smoothness of the density.