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XIII Symposium on Probability and Stochastic Processes

Part of the Progress in Probability Book Series (volume 75)

Editors: López, Sergio I.; Rivero, Víctor M.; Rocha-Arteaga, Alfonso; Siri-Jégousse, Arno

DOI: 10.1007/978-3-030-57513-7

ISBN: 978-3-030-57512-0

Publisher: Springer International Publishing - Springer Journals

Oct 17, 2020

1 - 6 of 6 Chapters

LitStream

Reflected (Degenerate) Diffusions and Stationary Measures

Duarte, Mauricio

Pages: 3 –35

[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...
LitStream

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

Angtuncio-Hernández, Osvaldo

Pages: 39 –65

[Random walks conditioned to stay positive are a prominent topic in fluctuation theory. One way to construct them is as a random walk conditioned to stay positive up to time n, and let n tend to infinity. A second method is conditioning instead to stay positive up to an independent geometric...
LitStream

A Berry–Esseen Type Theorem for Finite Free Convolution

Arizmendi, Octavio; Perales, Daniel

Pages: 67 –76

[We prove that the rate of convergence for the central limit theorem in finite free convolution is of order n−1∕2.]
LitStream

Predicting the Last Zero of a Spectrally Negative Lévy Process

Baurdoux, Erik J.; Pedraza, José M.

Pages: 77 –105

[Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the problem of finding a stopping time that minimises the...
LitStream

Box-Ball System: Soliton and Tree Decomposition of Excursions

Ferrari, Pablo A.; Gabrielli, Davide

Pages: 107 –152

[We review combinatorial properties of solitons of the Box-Ball system introduced by Takahashi and Satsuma (J Phys Soc Jpn 59(10):3514–3519, 1990). Starting with several definitions of the system, we describe ways to identify solitons and review a proof of the conservation of the solitons under...
LitStream

Invertibility of Infinitely Divisible Continuous-Time Moving Average Processes

Sauri, Orimar

Pages: 153 –167

[This paper studies the invertibility property of continuous time moving average processes driven by a Lévy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel involved and the characteristic triplet of the background...

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