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A transport process on graphs and its limiting distributions

Part of: Markov processes Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  10 October 2022

Leonardo Videla Open the ORCID record for Leonardo Videla [Opens in a new window]
Leonardo Videla*
Affiliation:
Universidad de Santiago de Chile
*
*Postal address: Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago, Chile. Email address: [email protected]
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Abstract

Given a finite strongly connected directed graph $G=(V, E)$ , we study a Markov chain taking values on the space of probability measures on V. The chain, motivated by biological applications in the context of stochastic population dynamics, is characterized by transitions between states that respect the structure superimposed by E: mass (probability) can only be moved between neighbors in G. We provide conditions for the ergodicity of the chain. In a simple, symmetric case, we fully characterize the invariant probability.

Keywords

Markov chains on the simplexDirichlet distribution

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces 60B10: Convergence of probability measures
Secondary: 92D25: Population dynamics (general) 92D40: Ecology
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 1 , March 2023 , pp. 341 - 357
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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