Hidden geometry of bi-directional grid constrained stochastic processes

Taranto, Aldo ORCID: https://orcid.org/0000-0001-6763-4997 and Khan, Shahjahan ORCID: https://orcid.org/0000-0002-0446-086X (2021) Hidden geometry of bi-directional grid constrained stochastic processes. arXiv Reprint. pp. 1-20.

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Abstract

Bi-Directional Grid Constrained (BGC) stochastic processes (BGCSP) are constrained Itô diffusions with the property that the further they drift away from the origin, the more resistance to movement in that direction they undergo. We investigate the underlying characteristics of the BGC parameter Ψ(x,t) by examining its geometric properties. The most appropriate convex form for Ψ, i.e. the parabolic cylinder is identified after extensive simulation of various possible forms. The formula for the resulting hidden reflective barrier(s) is determined by comparing it with the simpler Ornstein-Uhlenbeck process (OUP). Applications of BGCSP arise when a series of semipermeable barriers are present, such as regulating interest rates and chemical reactions under concentration gradients, which gives rise to two hidden reflective barriers.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: No
Item Status: Live Archive
Additional Information: Published version deposited in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -)
Faculty/School / Institute/Centre: Current - Institute for Advanced Engineering and Space Sciences (1 Aug 2018 -)
Date Deposited: 25 Mar 2021 05:19
Last Modified: 25 Mar 2021 05:19
Uncontrolled Keywords: bi-directional grid constrained (BGC) stochastic processes (BGCSP), Wiener processes, hidden barriers, stochastic differential equation (SDE), surfaces, contour plots, It^o diffusions, convex functions, Ornstein-Uhlenbeck process (OUP), vector fields
Fields of Research (2008): 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0104 Statistics > 010404 Probability Theory
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490510 Stochastic analysis and modelling
49 MATHEMATICAL SCIENCES > 4905 Statistics > 490503 Computational statistics
49 MATHEMATICAL SCIENCES > 4905 Statistics > 490506 Probability theory
URI: http://eprints.usq.edu.au/id/eprint/41637

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