Asymptotic behavior for an additive functional of two independent self-similar Gaussian processes
David Nualart, Fangjun Xu
TL;DR
This paper investigates the long-term behavior of an additive functional involving two independent self-similar Gaussian processes, utilizing the method of moments to analyze their intersection local time.
Contribution
It provides the first detailed asymptotic analysis of additive functionals for two independent self-similar Gaussian processes with existing intersection local time.
Findings
Derived the asymptotic behavior of the additive functional.
Established conditions for the existence of intersection local time.
Applied the method of moments to analyze the processes.
Abstract
We derive the asymptotic behavior for an additive functional of two independent self-similar Gaussian processes when their intersection local time exists, using the method of moments.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Scientific Research and Discoveries · Stochastic processes and financial applications