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      Bi-Directional Grid Constrained Stochastic Processes' Link to Multi-Skew Brownian Motion

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          Abstract

          Bi-Directional Grid Constrained (BGC) stochastic processes (BGCSPs) constrain the random movement toward the origin steadily more and more, the further they deviate from the origin, rather than all at once imposing reflective barriers, as does the well-established theory of It^o diffusions with such reflective barriers. We identify that BGCSPs are a variant rather than a special case of the multi-skew Brownian motion (M-SBM). This is because they have their own complexities, such as the barriers being hidden (not known in advance) and not necessarily constant over time. We provide an M-SBM theoretical framework and also a simulation framework to elaborate deeper properties of BGCSPs. The simulation framework is then applied by generating numerous simulations of the constrained paths and the results are analysed. BGCSPs have applications in finance and indeed many other fields requiring graduated constraining, from both above and below the initial position.

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          Author and article information

          Journal
          26 July 2021
          Article
          2107.12554
          3ef9f4d5-5259-46f9-b49f-1599ea8a1091

          http://creativecommons.org/licenses/by/4.0/

          History
          Custom metadata
          Manuscript accepted for publication in the Journal of Applied Probability & Statistics and will appear in issue 1 of volume 17 to be published in April 2022
          math.PR math.ST stat.AP stat.CO stat.TH

          Applications,Probability,Statistics theory,Mathematical modeling & Computation
          Applications, Probability, Statistics theory, Mathematical modeling & Computation

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