Diffusion spiders: Green kernel, excessive functions and optimal stopping

: Lempa Jukka, Mordecki Ernesto, Salminen Paavo

Publisher: ELSEVIER

: AMSTERDAM

: 2024

: Stochastic Processes and their Applications

: STOCHASTIC PROCESSES AND THEIR APPLICATIONS

: STOCH PROC APPL

: 104229

: 167

: 34

: 0304-4149

: 1879-209X

DOI: https://doi.org/10.1016/j.spa.2023.104229

: https://doi.org/10.1016/j.spa.2023.104229

: https://arxiv.org/abs/2209.11491

A diffusion spider is a strong Markov process with continuous paths taking values on a graph with one vertex and a finite number of edges (of infinite length). An example is Walsh's Brownian spider where the process on each edge behaves as a Brownian motion. In this paper we calculate firstly the density of the resolvent kernel in terms of the characteristics of the underlying diffusion. Excessive functions are studied via the Martin boundary theory. A crucial result is an expression for the representing measure of a given excessive function. These results are used to solve optimal stopping problems for diffusion spiders.(c) 2023 Elsevier B.V. All rights reserved.