Time Homogeneous Diffusion with drift and killing to meet a given marginal

TL;DR

This paper establishes conditions under which a time-homogeneous diffusion process with drift and killing can be constructed to match a specified marginal distribution at a fixed time.

Contribution

It provides new criteria linking probability measures, drift fields, and killing functions to realize desired marginals in diffusion processes.

Findings

Derived conditions for existence of such diffusion processes.

Characterized the relationship between drift, killing, and target marginals.

Extended the theory of Markov processes with killing to meet specified distributions.

Abstract

This article gives conditions on a probability measure and drift field b such that for a given killing field k and a given time t > 0, there is function a such that there is a time homogeneous Markov process with infinitesimal generator a((1/2)d^2/dx^2 + b d/dx - k) which meets the given marginal at time t.