Captive jump processes for bounded random systems with discontinuous dynamics

Name: Captive jump processes for bounded random systems with discontinuous dynamics
Author: Macrina, A., Mengütürk, L. A., Mengütürk, Murat Cahit

İsim	Captive jump processes for bounded random systems with discontinuous dynamics
Yazar	Macrina, A., Mengütürk, L. A., Mengütürk, Murat Cahit
Basım Tarihi:	2024-01
Basım Yeri	- Elsevier
Konu	Bounded domains, Captive processes, Dynamical systems, Jump–diffusion in continuous time, Monitored path-dependence, Simulation of stochastic process
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1007-5704
Kayıt Numarası	79f69bf7-7df5-4d4d-a9ab-dfaf2af1896d
Lokasyon	Business Administration
Tarih	2024-01
Örnek Metin	Stochastic captive jump processes are explicitly constructed in continuous time, whose non-linear dynamics are strictly confined by bounded domains that can be time-dependent. By introducing non-anticipative path-dependency, the framework offers the possibility of generating multiple inner tunnels within a master domain, such that a captive jump process is allowed to proceed either within a single inner tunnel or jump in between tunnels without ever penetrating the outermost shell. If a captive jump process is a continuous martingale or a pure-jump process, the uppermost confining boundary is non-decreasing, and the lowermost confining boundary is non-increasing. Under certain conditions, it can be shown that captive jump processes are invariant under monotonic transformations, enabling one to construct and study systems of increasing complexity using simpler building blocks. Amongst many applications, captive jump processes may be considered to model phenomena such as electrons transitioning from one orbit (valence shell) to another, quantum tunnelling where stochastic wave-functions can “penetrate” inner boundaries (i.e., walls) of potential energy, non-linear dynamical systems involving multiple attractors, and sticky concentration behaviour of pathogens in epidemics. We provide concrete, worked-out examples, and numerical simulations for the dynamics of captive jump processes within different geometries as demonstrations.
DOI	10.1016/j.cnsns.2023.107646
Cilt	128

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Captive jump processes for bounded random systems with discontinuous dynamics

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

Basım Tarihi 2024-01

Basım Yeri - Elsevier

Konu Bounded domains, Captive processes, Dynamical systems, Jump–diffusion in continuous time, Monitored path-dependence, Simulation of stochastic process

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1007-5704

Kayıt Numarası 79f69bf7-7df5-4d4d-a9ab-dfaf2af1896d

Lokasyon Business Administration

Tarih 2024-01

Örnek Metin Stochastic captive jump processes are explicitly constructed in continuous time, whose non-linear dynamics are strictly confined by bounded domains that can be time-dependent. By introducing non-anticipative path-dependency, the framework offers the possibility of generating multiple inner tunnels within a master domain, such that a captive jump process is allowed to proceed either within a single inner tunnel or jump in between tunnels without ever penetrating the outermost shell. If a captive jump process is a continuous martingale or a pure-jump process, the uppermost confining boundary is non-decreasing, and the lowermost confining boundary is non-increasing. Under certain conditions, it can be shown that captive jump processes are invariant under monotonic transformations, enabling one to construct and study systems of increasing complexity using simpler building blocks. Amongst many applications, captive jump processes may be considered to model phenomena such as electrons transitioning from one orbit (valence shell) to another, quantum tunnelling where stochastic wave-functions can “penetrate” inner boundaries (i.e., walls) of potential energy, non-linear dynamical systems involving multiple attractors, and sticky concentration behaviour of pathogens in epidemics. We provide concrete, worked-out examples, and numerical simulations for the dynamics of captive jump processes within different geometries as demonstrations.

DOI 10.1016/j.cnsns.2023.107646

Cilt 128