Author
Mengütürk, L. A., Mengütürk, Murat Cahit
Publication Date
2022-11-18
Publication Place
-
IOP Publishing
Subject
Captive dynamics, Coupled processes, Interacting systems, Stochastic domains
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
-s2.0-85142533506
Record ID
9b8ad2b2-bf00-48fc-bc70-8e317635e6e8
Library Location
Business Administration
Date
2022-11-18
Sample Text
We introduce a real-valued family of interacting diffusions where their paths can meet but cannot cross each other in a way that would alter their initial order. Any given interacting pair is a solution to coupled stochastic differential equations with time-dependent coefficients satisfying certain regularity conditions with respect to each other. These coefficients explicitly determine whether these processes bounce away from each other or stick to one another if/when their paths collide. When all interacting diffusions in the system follow a martingale behaviour, and if all these paths ultimately come into collision, we show that the system reaches a random steady-state with zero fluctuation thereafter. We prove that in a special case when certain paths abide to a deterministic trend, the system reduces down to the topology of captive diffusions. We also show that square-root diffusions form a subclass of the proposed family of processes. Applications include order-driven interacting particle systems in physics, adhesive microbial dynamics in biology and risk-bounded quadratic optimization solutions in control theory.
DOI
10.1088/1751-8121/aca188
Cilt
55
