Statistics of bounded processes driven by Poisson white noise
S.I. Denisov, Yu.S. Bystrik
TL;DR
This paper analyzes the statistical behavior of bounded jump processes driven by Poisson white noise, deriving their governing equations, finding exact stationary solutions, and validating results through simulations.
Contribution
It introduces a general framework for the stationary solutions of jump processes driven by Poisson noise within bounded domains, including exact solutions and numerical validation.
Findings
Derived the Kolmogorov-Feller equation for the process
Obtained exact stationary solutions in specific cases
Confirmed analytical results with numerical simulations
Abstract
We study the statistical properties of jump processes in a bounded domain that are driven by Poisson white noise. We derive the corresponding Kolmogorov-Feller equation and provide a general representation for its stationary solutions. Exact stationary solutions of this equation are found and analyzed in two particular cases. All our analytical findings are confirmed by numerical simulations.
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