Sensitivity analysis for diffusion processes constrained to an orthant

TL;DR

This paper investigates how diffusion processes constrained to the positive orthant respond to infinitesimal drift changes, providing unique solutions to an augmented Skorohod problem and establishing a fundamental adjoint relationship for their stationary distributions.

Contribution

It introduces a novel characterization of constrained diffusion functions and their drift-derivatives as solutions to an augmented Skorohod problem, advancing understanding of their sensitivity.

Findings

Unique solution to augmented Skorohod problem for constrained functions and derivatives

Establishment of a basic adjoint relationship for stationary distributions

Framework for analyzing sensitivity of constrained diffusion processes

Abstract

This paper studies diffusion processes constrained to the positive orthant under infinitesimal changes in the drift. Our first main result states that any constrained function and its (left) drift-derivative is the unique solution to an augmented Skorohod problem. Our second main result uses this characterization to establish a basic adjoint relationship for the stationary distribution of the constrained diffusion process jointly with its left-derivative process.