Iterated logarithm bounds of bi-directional grid constrained stochastic processes
Article
Article Title | Iterated logarithm bounds of bi-directional grid constrained stochastic processes |
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Article Category | Article |
Authors | Taranto, Aldo (Author), Khan, Shahjahan (Author) and Addie, Ron (Author) |
Journal Title | Global and Stochastic Analysis |
Journal Citation | 8 (3), pp. 19-39 |
Number of Pages | 21 |
Year | 2021 |
Publisher | MUK Publications |
Place of Publication | Qarshi, Uzbekistan |
ISSN | 2248-9444 |
Web Address (URL) | https://www.mukpublications.com/resources/2_CSA_Taranto_A_OK_compressed.pdf |
Abstract | We derive a novel framework called Bi-Directional Grid Constrained (BGC) stochastic processes in which the further an Itô 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 Itô diffusions for a representative expression for λ(X, t), both before and after BGC and uncover some interesting results with applications into finance and many other areas. |
Keywords | Wiener Process, Itˆo Processes, Law of Iterated Logarithm (LIL), Bi-Directional Grid Constrained (BGC) Stochastic Processes, hidden barriers |
Contains Sensitive Content | Does not contain sensitive content |
ANZSRC Field of Research 2020 | 490510. Stochastic analysis and modelling |
490506. Probability theory | |
490399. Numerical and computational mathematics not elsewhere classified | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions, but may be accessed online. Please see the link in the URL field. |
Byline Affiliations | School of Sciences |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q6v0q/iterated-logarithm-bounds-of-bi-directional-grid-constrained-stochastic-processes
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