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Simulation of a simple particle system interacting through hitting times

Abstract:
We develop an Euler-type particle method for the simulation of a McKean–Vlasov equation arising from a mean-field model with positive feedback from hitting a boundary. Under assumptions on the parameters which ensure differentiable solutions, we establish convergence of order 1/2 in the time step. Moreover, we give a modification of the scheme using Brownian bridges and local mesh refinement, which improves the order to 1. We confirm our theoretical results with numerical tests and empirically investigate cases with blow-up.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.3934/dcdsb.2019067

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Institution:
University of Oxford
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Catherine's College
Role:
Author
ORCID:
0000-0003-4027-5298
Publisher:
American Institute of Mathematical Sciences Publisher's website
Journal:
Discrete and Continuous Dynamical Systems - Series B Journal website
Volume:
24
Issue:
10
Pages:
5481-5502
Publication date:
2019-04-30
Acceptance date:
2018-10-29
DOI:
EISSN:
1553-524X
ISSN:
1531-3492
Source identifiers:
948543
Language:
English
Keywords:
Pubs id:
pubs:948543
UUID:
uuid:18d18733-bfca-480a-aede-c0ea97c05b7f
Local pid:
pubs:948543
Deposit date:
2018-11-30

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