Captive diffusions and their applications to order-preserving dynamics
Type :
Article
Publication Status :
Published
Access :
openAccess
Abstract
We propose a class of stochastic processes that we call captive diffusions, which evolve within measurable pairs of cadlag bounded functions that admit bounded right-derivatives at points where they are continuous. In full generality, such processes allow reflection and absorption dynamics at their boundaries-possibly in a hybrid manner over non-overlapping time periods-and if they are martingales, continuous boundaries are necessarily monotonic. We employ multi-dimensional captive diffusions equipped with a totally ordered set of boundaries to model random processes that preserve an initially determined rank. We run numerical simulations on several examples governed by different drift and diffusion coefficients. Applications include interacting particle systems, random matrix theory, epidemic modelling and stochastic control.
Source :
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Date :
2020-09-30
Volume :
476
Issue :
2241
Publisher :
Royal Society Publishing
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