Journal article
Analytic continuation of time in Brownian motion. Stochastic distributions approach
Journal of mathematical analysis and applications, Vol.558(1), 130438
06/01/2026
DOI: 10.1016/j.jmaa.2026.130438
Abstract
With the use of Hida's white noise space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian processes, with focus here on Brownian motion. For the latter, we prove and make use of bounds in the complex plane for the Hermite functions; as well as a new approach to stochastic distributions. This in turn allows us to present (in Section 6) an explicit formula for an analytically continued white noise process, realized this way in the complex domain. With the use of the Wick product, we then apply our complex white noise analysis in Section 7 in a derivation of a new realization of Hilbert space-valued stochastic integrals.
Details
- Title: Subtitle
- Analytic continuation of time in Brownian motion. Stochastic distributions approach
- Creators
- Luis Daniel Abreu - University of ViennaDaniel Alpay - Chapman UniversityTryphon Georgiou - University of California, IrvinePalle Jorgensen - Department of Mathematics, 14 MLH, The University of Iowa, Iowa City, IA 52242-1419, USA
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical analysis and applications, Vol.558(1), 130438
- DOI
- 10.1016/j.jmaa.2026.130438
- ISSN
- 0022-247X
- eISSN
- 1096-0813
- Publisher
- Elsevier Inc
- Grant note
- the Foster G. and Mary McGaw Professorship in Mathematical Sciences W911NF-22-1-0292 / ARO (https://doi.org/10.13039/100000183) ECCS-2347357 / NSF (https://doi.org/10.13039/100000001) FA9550-24-1-0278 / AFOSR (https://doi.org/10.13039/100000181)
- Language
- English
- Electronic publication date
- 01/15/2026
- Date published
- 06/01/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985130219402771
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