Hidden geometry of bidirectional 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 bidirectional grid-constrained stochastic processes. Journal of Probability and Statistics, 2021:9944543. pp. 1-13. ISSN 1687-952X


Abstract

Bidirectional Grid Constrained (BGC) stochastic processes (BGCSPs) are constrained Ito diffusions with the property that the further they drift away from the origin, the more the resistance to movement in that direction they undergo. The underlying characteristics of the BGC parameter Psi(X-t, t) are investigated by examining its geometric properties. The most appropriate convex form for Psi, that is, 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.


Statistics for USQ ePrint 43878
Statistics for this ePrint Item
Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to Published version 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 - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -)
Date Deposited: 19 Oct 2021 02:57
Last Modified: 10 Nov 2021 00:35
Uncontrolled Keywords: dimensional random-walk
Fields of Research (2008): 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
01 Mathematical Sciences > 0104 Statistics > 010404 Probability Theory
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010399 Numerical and Computational Mathematics not elsewhere classified
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490510 Stochastic analysis and modelling
49 MATHEMATICAL SCIENCES > 4905 Statistics > 490506 Probability theory
49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490399 Numerical and computational mathematics not elsewhere classified
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Socio-Economic Objectives (2020): 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences
Identification Number or DOI: https://doi.org/10.1155/2021/9944543
URI: http://eprints.usq.edu.au/id/eprint/43878

Actions (login required)

View Item Archive Repository Staff Only