On a family of coupled diffusions that can never change their initial order

Name: On a family of coupled diffusions that can never change their initial order
Author: Mengütürk, L. A., Mengütürk, Murat Cahit

İsim	On a family of coupled diffusions that can never change their initial order
Yazar	Mengütürk, L. A., Mengütürk, Murat Cahit
Basım Tarihi:	2022-11-18
Basım Yeri	- IOP Publishing
Konu	Captive dynamics, Coupled processes, Interacting systems, Stochastic domains
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	-s2.0-85142533506
Kayıt Numarası	9b8ad2b2-bf00-48fc-bc70-8e317635e6e8
Lokasyon	Business Administration
Tarih	2022-11-18
Örnek Metin	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

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On a family of coupled diffusions that can never change their initial order

Yazar Mengütürk, L. A., Mengütürk, Murat Cahit

Basım Tarihi 2022-11-18

Basım Yeri - IOP Publishing

Konu Captive dynamics, Coupled processes, Interacting systems, Stochastic domains

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası -s2.0-85142533506

Kayıt Numarası 9b8ad2b2-bf00-48fc-bc70-8e317635e6e8

Lokasyon Business Administration

Tarih 2022-11-18

Örnek Metin 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