mu-Brownian Motion, Dualities, Diffusions, Transforms, and Reproducing Kernel Hilbert Spaces

Daniel Alpay () and Palle Jorgensen ()
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Daniel Alpay: Chapman University
Palle Jorgensen: The University of Iowa

Journal of Theoretical Probability, 2022, vol. 35, issue 4, 2757-2783

Abstract: Abstract Replacing the Lebesgue measure on an interval by a Stieltjes positive non-atomic measure, we study the corresponding counterpart of the Brownian motion. We introduce a new heat equation associated with the measure and make connections with stationary-increments Gaussian processes. We introduce a new transform analysis, and heat equation, associated with the measure, and make connections here too with stationary-increments and stationary Gaussian processes. In the main result of this paper (Theorem 7.2), we use white noise space analysis to derive a new heat equation associated with a (wide class of) stationary-increments Gaussian processes.

Keywords: Gaussian processes; Stationary square-increments; Itô calculus; Malliavin derivative; Stochastic Fourier transform; Diffusion; Fractal; White noise space analysis; Reproducing kernels; 60J22; 60J70; 46E22 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01146-w

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