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Diffusion spiders: Green kernel, excessive functions and optimal stopping
Tekijät: Lempa Jukka, Mordecki Ernesto, Salminen Paavo
Kustantaja: ELSEVIER
Kustannuspaikka: AMSTERDAM
Julkaisuvuosi: 2024
Journal: Stochastic Processes and their Applications
Tietokannassa oleva lehden nimi: STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Lehden akronyymi: STOCH PROC APPL
Artikkelin numero: 104229
Vuosikerta: 167
Sivujen määrä: 34
ISSN: 0304-4149
eISSN: 1879-209X
DOI: https://doi.org/10.1016/j.spa.2023.104229
Verkko-osoite: https://doi.org/10.1016/j.spa.2023.104229
Preprintin osoite: https://arxiv.org/abs/2209.11491
Tiivistelmä
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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