A1 Refereed original research article in a scientific journal
Diffusion spiders: Green kernel, excessive functions and optimal stopping
Authors: Lempa Jukka, Mordecki Ernesto, Salminen Paavo
Publisher: ELSEVIER
Publishing place: AMSTERDAM
Publication year: 2024
Journal: Stochastic Processes and their Applications
Journal name in source: STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Journal acronym: STOCH PROC APPL
Article number: 104229
Volume: 167
Number of pages: 34
ISSN: 0304-4149
eISSN: 1879-209X
DOI: https://doi.org/10.1016/j.spa.2023.104229
Web address : https://doi.org/10.1016/j.spa.2023.104229
Preprint address: https://arxiv.org/abs/2209.11491
Abstract
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.
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.
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