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2020 | OriginalPaper | Chapter

Reflected (Degenerate) Diffusions and Stationary Measures

Author : Mauricio Duarte

Published in: XIII Symposium on Probability and Stochastic Processes

Publisher: Springer International Publishing

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Abstract

These notes were written with the occasion of the XIII Symposium on Probability and Stochastic Processes at UNAM. We will introduce general reflected diffusions with instantaneous reflection when hitting the boundary. Two main tools for studying these processes are presented: the submartingale problem, and stochastic differential equations. We will see how these two complement each other. In the last sections, we will see in detail two processes to which this theory applies nicely, and uniqueness of a stationary distribution holds for them, despite the fact they are degenerate.

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next chapter Multidimensional Random Walks Conditioned to Stay Ordered via Generalized Ladder Height Functions

These notes were written for a four-lecture mini-course at the XIII Symposium on Probability and Stochastic Processes, held at the Faculty of Sciences, Universidad Nacional Autónoma de México, from December 4–8, 2017.

This is a good exercise in stochastic calculus. I recommend to follow it closely, and fill the minor gaps.

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Title: Reflected (Degenerate) Diffusions and Stationary Measures
Author: Mauricio Duarte
Publisher: Springer International Publishing
Book: XIII Symposium on Probability and Stochastic Processes
Print ISBN: 978-3-030-57512-0

Electronic ISBN: 978-3-030-57513-7

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-57513-7_1