Boundary Classification of Diffusion Processes via Local Time for the Stroock-Williams Problem

Abstract

In [13] Daniel Stroock and David Williams introduced the following initial boundary value problem \begin{align} &u_t(t,x)=\mu u_x(t,x) + \frac{1}{2} u_{xx}(t,x) \h{2cm} &(t,x) \in (0,\infty) \times [0,\infty) \label{1a}\\ &u(0,x)=f(x) &x \in [0,\infty) \label{2a}\\ &u_t(t,0)=\nu u_x(t,0) &t \in (0,\infty)\label{3a} \end{align} where $\mu, \nu \in \mathbb{R}$, paying particular attention to the peculiar characteristics at the boundary $x=0$ in the case that $\nu

Date of Award	5 Feb 2025
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Goran Peskir (Main Supervisor) & Peter Johnson (Co Supervisor)