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The physical mechanism of stochastic calculus in random walks

Authors
  • Lee, Chern
  • Ye, Hai
  • Li, Hui
Type
Published Article
Journal
Journal of Statistical Mechanics: Theory and Experiment
Publisher
IOP Publishing
Publication Date
Feb 13, 2024
Volume
2024
Issue
2
Identifiers
DOI: 10.1088/1742-5468/ad1be1
Source
ioppublishing
Keywords
Disciplines
  • Paper section: Classical statistical mechanics, equilibrium and non-equilibrium
License
Unknown

Abstract

Stochastic differential equations (SDEs) play an important role in fields ranging from physics and biology to economics. The interpretation of stochastic calculus in the presence of multiplicative noise continues to be an open question. Commonly, the choice of stochastic calculus rules is largely based on empirical knowledge and lacks quantitative substantiation. In this study, we introduce a functional method that quantitatively links stochastic calculus rules to the underlying physical mechanisms in random walks. For a given diffusion coefficient, we construct three models to exemplify the physical features of conventional stochastic calculus. Our work provides a new perspective for quantitatively addressing state-dependent noise and aims to contribute to the understanding of the physical factors underlying uncertainty in SDEs.

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