Buongiorno a tutt*
ho il piacere di annunciare il prossimo webinar del ciclo di seminari online
promosso dal Gruppo UMI PRISMA (http://www.umi-prisma.polito.it/index.html).
*Lunedì 6 marzo 2023, *
*ore 16-17 Alessandro Calvia*
*Titolo: *Stochastic filtering in a non-Markovian framework with predictable jump times.
*Abstract:* Stochastic filtering is a classic branch of applied probability. Research on this subject began with the pioneering works of N. Wiener and R. E. Kalman; since then, it has vastly expanded in numerous directions and is still ongoing. The starting point of a stochastic filtering problem is a partially observed system, i.e., a model consisting of a signal (or unobserved) process and an observed process. The main goal is to compute an equation satisfied by the filter, which is the conditional distribution of the hidden signal given the available observation. To deduce filtering equations, classic models usually feature Markovian signal-observation pairs that may only have totally inaccessible jump times. In this talk I will present a non-Markovian model, with path-dependent coefficients, that also allows for predictable jump times both in the signal and in the observed process. These two features naturally arise in various applications and require some new ideas and non-trivial technical tools to be dealt with in the context of stochastic filtering. After providing some examples, I will deduce the filtering equation and, if time permits, I will discuss some possible future research. This is joint work with Elena Bandini and Katia Colaneri.
*ore 17-18 **Massimiliano Gubinelli*
*Titolo:* What is stochastic quantisation?
*Abstract:* Euclidean quantum fields (EQFs) are probability measures on spaces of generalized functions on R^d out of which one can construct quantum field theories via a well understood procedure. Proving the existence of non-Gaussian Euclidean quantum fields in dimensions d=2,3 has been proved quite challenging, and informed the development of new mathematical techniques (logarithmic Sobolev inequalities, phase-space expansion, cluster and polymer expansions, renormalization group). More recently, also thanks to development in the theory of singular stochastic partial differential equations, the study of these probability measures has been taken on again, from the point of view of stochastic analysis. I will try to give a broad panorama of this stochastic approach, of his results and of the many open problems. As a result I would like to motivate the idea that stochastic quantisation should be seen as a novel kind of stochastic analysis adapted to situations, like EQFs, where stochastic calculus alone is not effective due to singular nature of the objects or the lack of a useful filtration.
Qui di seguito il link per la partecipazione:
https://teams.microsoft.com/l/meetup-join/19%3ad685b25ed15f4821ac5168e63cf98...
Cari saluti,
Claudia Ceci
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Claudia Ceci
Dipartimento di Metodi e Modelli per l’Economia, il Territorio e la Finanza (MEMOTEF)
Università di Roma La Sapienza Via Del Castro Laurenziano 9 Roma 00161 Italy
Email: claudia.ceci@uniroma1.it