Trivariate distribution of sticky Brownian motion
Jean-Baptiste Casteras, L\'eonard Monsaingeon
TL;DR
This paper derives a closed-form expression for the joint distribution of position, local time, and occupation time of one-dimensional sticky Brownian motion, addressing gaps and errors in previous literature.
Contribution
It provides the first explicit formula for the trivariate distribution of sticky Brownian motion's key stochastic quantities.
Findings
Closed-form trivariate distribution derived
Addresses and corrects previous literature gaps
Enhances understanding of sticky Brownian motion behavior
Abstract
In this short note we derive a closed form for the trivariate distribution (position, local time at the origin, and positive occupation time) of the one-dimensional sticky Brownian motion, thereby filling some gaps and fixing some mistakes in the literature.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Complex Systems and Time Series Analysis · Mathematical Dynamics and Fractals