Iterated Logarithm Bounds 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 and Addie, Ron (2021) Iterated Logarithm Bounds of Bi-Directional Grid Constrained Stochastic Processes. arXiv, 3 Mar 2021. pp. 1-21.

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Abstract

We derive a novel framework called Bi-Directional Grid Constrained (BGC) stochastic processes in which the further an Ito diffusion drifts away from the origin, then the further it will be constrained. By making suitable modifications to the Law of Iterated Logarithm (LIL), we derive a novel theorem about the upper and lower bounds for BGC processes and their hidden barrier. To visualize the theorem, we run many simulations of the Ito diffusions for a representative expression for lambda(X, t), both before and after BGC and uncover some interesting results with applications into finance and many other areas.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: No
Item Status: Live Archive
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: 10 Mar 2021 23:32
Last Modified: 10 Mar 2021 23:32
Uncontrolled Keywords: Ito diffusions; Law of Iterated Logarithm (LIL); Bi-Directional Grid Constrained (BGC)stochastic processes
Fields of Research (2008): 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
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 > 4903 Numerical and computational mathematics > 490303 Numerical solution of differential and integral equations
49 MATHEMATICAL SCIENCES > 4905 Statistics > 490506 Probability theory
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970114 Expanding Knowledge in Economics
E Expanding Knowledge > 97 Expanding Knowledge > 970108 Expanding Knowledge in the Information and Computing Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Socio-Economic Objectives (2020): 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280108 Expanding knowledge in economics
28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280115 Expanding knowledge in the information and computing sciences
28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences
URI: http://eprints.usq.edu.au/id/eprint/41542

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