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Seminar on stochastic processes

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Spring Semester 2024

Date / Time Speaker Title Location
6 March 2024
17:15-18:15 		Prof. Dr. Vincent Vargas
Universität Genf
Event Details

Seminar on Stochastic Processes

Title Harmonic analysis of Gaussian multiplicative chaos on the circle
Speaker, Affiliation Prof. Dr. Vincent Vargas, Universität Genf
Date, Time 6 March 2024, 17:15-18:15
Location HG G 43
Abstract Gaussian multiplicative chaos (GMC) on the circle is a canonical (random) multifractal measure on the circle which appears in a wide variety of contexts and most recently in relation to Liouville conformal field theory. In this talk, I will present the first results concerning the decay and renormalization of the Fourier coefficients of GMC. In particular, one can show that GMC is a so-called Rajchman measure which means that its Fourier coefficients go to zero when the frequency goes to infinity. Numerous questions remain open. Based on a joint work with C. Garban.
Harmonic analysis of Gaussian multiplicative chaos on the circleread_more (CANCELLED)
HG G 43
13 March 2024
17:15-18:15 		Dr. Victor Rivero
CIMAT Guanajuato
Event Details

Seminar on Stochastic Processes

Title Recurrent extensions and Stochastic Differential equations
Speaker, Affiliation Dr. Victor Rivero, CIMAT Guanajuato
Date, Time 13 March 2024, 17:15-18:15
Location HG G 43
Abstract In the 70's Itô settled the excursion theory of Markov processes, which is nowadays a fundamental tool for analyzing path properties of Markov processes. In his theory, Itô also introduced a method for building Markov processes using the excursion data, or by gluing excursions together, the resulting process is known as the recurrent extension of a given process. Since Itô's pioneering work the method of recurrent extensions has been added to the toolbox for building processes, which of course includes the martingale problem and stochastic differential equations. The latter are among the most popular tools for building and describing stochastic processes, in particular in applied models as they allow to physically describe the infinitesimal variations of the studied phenomena. In this work we answer the following natural question. Assume X is a Markov process taking values in R that dies at the first time it hits a distinguished point of the state space, say 0, which happens in a finite time a.s., that X satisfies a stochastic differential equation, and finally that X admits a recurrent extension, say Z, is a processes that behaves like Z up to the first hitting time of 0, and for which 0 is a recurrent and regular state. If any, what is the SDE satisfied by Z? Our answer to this question allows us to describe the SDE satisfied by many Feller processes. We analyze various particular examples, as for instance the so-called Feller brownian motions and diffusions, which include their sticky and skewed versions, and also continuous state branching processes and spectrally positive Levy processes.
Recurrent extensions and Stochastic Differential equationsread_more
HG G 43
20 March 2024
17:15-18:15 		Dr. Jean-Jil Duchamps
Université de Franche-Comté / Besançon
Event Details

Seminar on Stochastic Processes

Title Local weak convergence for a general stochastic SIR model
Speaker, Affiliation Dr. Jean-Jil Duchamps, Université de Franche-Comté / Besançon
Date, Time 20 March 2024, 17:15-18:15
Location HG G 43
Abstract We study an epidemiological model where infections arise in a population according to a general, non-Markovian SIR-like model with a time-dependent contact rate. We make few assumptions, only requiring that the number of potential infections generated by an individual has finite expectation on bounded time intervals. This model can be viewed as a general Crump-Mode-Jagers model with interactions, and we study the local weak convergence of its infection graph, which yields (1) a functional law of large numbers for our SIR process, and (2) the identification of a "contact-tracing Markov process" that traces back the chain of infection leading to a typical individual. This is joint work with Félix Foutel-Rodier and Emmanuel Schertzer.
Local weak convergence for a general stochastic SIR modelread_more
HG G 43
10 April 2024
17:15-18:15 		Dr. Hugo Vanneuville
CNRS, Université Grenoble Alpes
Event Details

Seminar on Stochastic Processes

Title Exponential decay for Bernoulli percolation via stochastic comparison
Speaker, Affiliation Dr. Hugo Vanneuville, CNRS, Université Grenoble Alpes
Date, Time 10 April 2024, 17:15-18:15
Location HG G 43
Abstract Bernoulli percolation of parameter p on Z^d is defined by deleting each edge of Z^d with probability 1-p, independently of the other edges. The exponential decay theorem - proven in the 80's by Menshikov and, independently, by Aizenman and Barsky - can be stated as follows: If the cardinality of the cluster of 0 is a.s. finite at some parameter p, then it has an exponential moment at every parameter q
Exponential decay for Bernoulli percolation via stochastic comparisonread_more
HG G 43
17 April 2024
17:15-18:15 		Prof. Dr. Vincent Vargas
Universität Genf
Event Details

Seminar on Stochastic Processes

Title Harmonic analysis of Gaussian multiplicative chaos on the circle
Speaker, Affiliation Prof. Dr. Vincent Vargas, Universität Genf
Date, Time 17 April 2024, 17:15-18:15
Location HG G 43
Abstract Gaussian multiplicative chaos (GMC) on the circle is a canonical (random) multifractal measure on the circle which appears in a wide variety of contexts and most recently in relation to Liouville conformal field theory. In this talk, I will present the first results concerning the decay and renormalization of the Fourier coefficients of GMC. In particular, one can show that GMC is a so-called Rajchman measure which means that its Fourier coefficients go to zero when the frequency goes to infinity. Numerous questions remain open. Based on a joint work with C. Garban.
Harmonic analysis of Gaussian multiplicative chaos on the circleread_more (CANCELLED)
HG G 43
15 May 2024
17:15-18:15 		Dr. Geronimo Uribe Bravo
Universidad Nacional Autónoma de México
Event Details

Seminar on Stochastic Processes

Title A pathwise approach to time change
Speaker, Affiliation Dr. Geronimo Uribe Bravo, Universidad Nacional Autónoma de México
Date, Time 15 May 2024, 17:15-18:15
Location HG G 43
Abstract Time-change equations are a generalization of ordinary differential equations which are driven by the random, irregular, and possibly densely discontinuous sample paths of the typical stochastic process. They can be thought of as a multiparameter version of the method of time-change and can be given a pathwise theory. Time-change equations can lead to deep results on weak existence and uniqueness of stochastic differential equations and posses a robust strong approximation theory. However, time-change equations are not restricted to Markovian or semimartingale settings. In this talk, we will go through some examples of time-change equations which can be succesfully analyzed (such as (multidimensional) affine processes, sticky Lévy processes or Doeblin´s mostly unknown proposal for diffusion processes) as well as some open problems they suggest.
A pathwise approach to time changeread_more
HG G 43
29 May 2024
17:15-18:15 		Prof. Dr. Serte Donderwinkel
University of Groningen
Event Details

Seminar on Stochastic Processes

Title Title T.B.A.
Speaker, Affiliation Prof. Dr. Serte Donderwinkel, University of Groningen
Date, Time 29 May 2024, 17:15-18:15
Location HG G 43
Title T.B.A.
HG G 43

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