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

Daniel Alpay, Palle Jorgensen

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)2757-2783
Number of pages27
JournalJournal of Theoretical Probability
Volume35
Issue number4
DOIs
StatePublished - 1 Dec 2022
Externally publishedYes

Keywords

  • Diffusion
  • Fractal
  • Gaussian processes
  • Itô calculus
  • Malliavin derivative
  • Reproducing kernels
  • Stationary square-increments
  • Stochastic Fourier transform
  • White noise space analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'mu-Brownian Motion, Dualities, Diffusions, Transforms, and Reproducing Kernel Hilbert Spaces'. Together they form a unique fingerprint.

Cite this