Weak solutions to gamma-driven stochastic differential equations

TL;DR

This paper investigates the existence of weak solutions for gamma-driven stochastic differential equations, providing conditions on volatility functions and analyzing the density process between different solution laws.

Contribution

It introduces new conditions for weak solution existence and characterizes the density process between solutions with varying volatility functions.

Findings

Established existence criteria for weak solutions.

Analyzed the density process between solutions with different volatilities.

Provided theoretical insights into gamma-driven SDEs.

Abstract

We study a stochastic differential equation driven by a gamma process, for which we give results on the existence of weak solutions under conditions on the volatility function. To that end we provide results on the density process between the laws of solutions with different volatility functions.