Local time and Tanaka formula for a Volterra-type multifractional Gaussian process
Brahim Boufoussi, Marco Dozzi, Renaud Marty
TL;DR
This paper develops a Tanaka formula and studies the local time properties of a Volterra-type multifractional Gaussian process using stochastic calculus and Fourier analysis.
Contribution
It introduces a Tanaka formula for this specific Gaussian process and analyzes the existence and regularity of its local time, extending stochastic calculus tools.
Findings
Tanaka formula derived for the process
Existence of local time established
Regularity properties of local time analyzed
Abstract
The stochastic calculus for Gaussian processes is applied to obtain a Tanaka formula for a Volterra-type multifractional Gaussian process. The existence and regularity properties of the local time of this process are obtained by means of Berman's Fourier analytic approach.
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Taxonomy
TopicsComplex Systems and Time Series Analysis · Stochastic processes and financial applications · Advanced Thermodynamics and Statistical Mechanics