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Stochastic Mean-Field Dynamics and Applications to Life Sciences Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Stochastic Duality and Eigenfunctions

Authors : Frank Redig, Federico Sau

Published in: Stochastic Dynamics Out of Equilibrium

Publisher: Springer International Publishing

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Abstract

We start from the observation that, anytime two Markov generators share an eigenvalue, the function constructed from the product of the two eigenfunctions associated to this common eigenvalue is a duality function. We push further this observation and provide a full characterization of duality relations in terms of spectral decompositions of the generators for finite state space Markov processes. Moreover, we study and revisit some well-known instances of duality, such as Siegmund duality, and extract spectral information from it. Next, we use the same formalism to construct all duality functions for some solvable examples, i.e., processes for which the eigenfunctions of the generator are explicitly known.

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previous chapter A Rate of Convergence Result for the Frederickson-Andersen Model
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Metadata
Title
Stochastic Duality and Eigenfunctions
Authors
Frank Redig
Federico Sau
Copyright Year
2019
Book
Stochastic Dynamics Out of Equilibrium

Print ISBN: 978-3-030-15095-2

Electronic ISBN: 978-3-030-15096-9

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-15096-9_25