Local Time in Parisian Walkways
Jir\^o Akahori
TL;DR
This paper investigates the properties of a special symmetric random walk called the Parisian walk in the complex plane, focusing on deriving Ito and Tanaka formulas related to its local time, which measures exit counts from regions.
Contribution
It introduces and analyzes the Ito and Tanaka formulas for Parisian walks, a novel class of symmetric random walks in the complex plane, with a focus on local time characterization.
Findings
Derived Ito formula for Parisian walk local time
Established Tanaka formula for the same class of walks
Provided insights into exit count behavior of the walk
Abstract
In the present paper, Ito formula and Tanaka formula for a special kind of symmetric random walk in the complex plain are studied. The random walk is called Parisian walk, and its local time is defined to be the number of exit from some regions.
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Taxonomy
TopicsPublic Spaces through Art · Financial Crisis of the 21st Century · French Urban and Social Studies