Author
Mengütürk, L. A., Mengütürk, Murat Cahit
Publication Date
2020-09-30
Publication Place
-
Royal Society Publishing
Subject
Markov processes, Bounded diffusions, Degenerate processes, Stochastic volatility
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1364-5021
Record ID
992e39f0-df6d-4e9a-ad11-e0f366548919
Library Location
Business Administration
Date
2020-09-30
Sample Text
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.
DOI
10.1098/rspa.2020.0294
Cilt
476
