Non-mean-field Vicsek-type models for collective behaviour

Autor: Paolo Buttà, Ben Goddard, Thomas M. Hodgson, Michela Ottobre, Kevin J. Painter

Publikováno v: Buttà, P, Goddard, B D, Hodgson, T, Ottobre, M & Painter, K J 2023, ' Non-mean-field Vicsek-type models for collective behaviour ', Mathematical Models and Methods in Applied Sciences, vol. 32, no. 14, pp. 2763-2816 . https://doi.org/10.1142/S0218202522500646

We consider interacting particle dynamics with Vicsek type interactions, and their macroscopic PDE limit, in the non-mean-field regime; that is, we consider the case in which each particle/agent in the system interacts only with a prescribed subset o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::70a44dd34667fbdce3e4035fed76988b
https://www.pure.ed.ac.uk/ws/files/348572495/2206.06776.pdf

Fast non mean-field networks: uniform in time averaging

Autor: Julien Barré, Ewelina Zatorska, Michela Ottobre, Paul Dobson

We study a population of $N$ particles, which evolve according to a diffusion process and interact through a dynamical network. In turn, the evolution of the network is coupled to the particles' positions. In contrast with the mean-field regime, in w

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::462939834f8d144bab327038b0581bb4
http://arxiv.org/abs/2003.14230

Uniform in time estimates for the weak error of the Euler method for SDEs and a Pathwise Approach to Derivative Estimates for Diffusion Semigroups

Autor: Dan Crisan, Michela Ottobre, Paul Dobson

We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires i) exponential decay in time of the space-derivatives of the semigroup associated with t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df36c0caf4322e88857b935568ab7762
http://arxiv.org/abs/1905.03524

Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes

Autor: Michela Ottobre, Thomas Cass, Paul Dobson, Dan Crisan

Publikováno v: Electronic Journal of Probability, 26

We study the long time behaviour of a large class of diffusion processes on $R^N$, generated by second order differential operators of (possibly) degenerate type. The operators that we consider {\em need not} satisfy the H\"ormander condition. Instea

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d573a0e4ef97f89a9d1f054adba98ea5

Some remarks on degenerate hypoelliptic Ornstein-Uhlenbeck operators

Autor: Karel Pravda-Starov, Grigorios A. Pavliotis, Michela Ottobre

Publikováno v: Journal of Mathematical Analysis and applications
Journal of Mathematical Analysis and applications, Elsevier, 2015, 429 (2), pp.676-712. 〈10.1016/j.jmaa.2015.04.019〉
Journal of Mathematical Analysis and Applications
Journal of Mathematical Analysis and Applications, Elsevier, 2015, 429 (2), pp.676-712. ⟨10.1016/j.jmaa.2015.04.019⟩
Journal of Mathematical Analysis and Applications, 2015, 429 (2), pp.676-712. ⟨10.1016/j.jmaa.2015.04.019⟩

We study degenerate hypoelliptic Ornstein-Uhlenbeck operators in $L^2$ spaces with respect to invariant measures. The purpose of this article is to show how recent results on general quadratic operators apply to the study of degenerate hypoelliptic O

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::67c9670d3c4a58a06486b2b844595a92
https://hal.archives-ouvertes.fr/hal-01110692