Hidden Geometry of Bidirectional Grid-Constrained Stochastic Processes

Bidirectional Grid Constrained (BGC) stochastic processes (BGCSPs) are constrained Itô 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 ΨXt,t are inve...

Full description

Saved in:
Bibliographic Details
Published inJournal of Probability and Statistics Vol. 2021; pp. 1 - 13
Main Authors Taranto, Aldo, Khan, Shahjahan
Format Journal Article
LanguageEnglish
Published New York Hindawi 25.05.2021
Hindawi Limited
Wiley
Subjects
Algorithms
Artificial intelligence
Chemical reactions
Concentration gradient
Convex analysis
Diffusion
Game theory
Geometry
Interest rates
Partial differential equations
Probability
Queuing theory
Random variables
Stochastic models
Stochastic processes
Online AccessGet full text

Cover

More Information
Summary:Bidirectional Grid Constrained (BGC) stochastic processes (BGCSPs) are constrained Itô 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 ΨXt,t are investigated by examining its geometric properties. The most appropriate convex form for Ψ, 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.
ISSN:1687-952X
1687-9538
DOI:10.1155/2021/9944543