Journal article
mu-Brownian Motion, Dualities, Diffusions, Transforms, and Reproducing Kernel Hilbert Spaces
Journal of theoretical probability, Vol.35(4), pp.2757-2783
12/2022
DOI: 10.1007/s10959-021-01146-w
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.
Details
- Title: Subtitle
- mu-Brownian Motion, Dualities, Diffusions, Transforms, and Reproducing Kernel Hilbert Spaces
- Creators
- Daniel Alpay - Chapman UniversityPalle Jorgensen - Univ Iowa, Dept Math, 14 MLH, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Journal of theoretical probability, Vol.35(4), pp.2757-2783
- DOI
- 10.1007/s10959-021-01146-w
- ISSN
- 0894-9840
- eISSN
- 1572-9230
- Publisher
- SPRINGER/PLENUM PUBLISHERS
- Number of pages
- 27
- Grant note
- Foster G. and Mary McGaw Professorship in Mathematical Sciences
- Language
- English
- Electronic publication date
- 01/24/2022
- Date published
- 12/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984241042602771
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