A probabilistic interpretation to the symmetries of a discrete heat equation

Research output: Chapters, Conference Papers, Creative and Literary WorksRGC 32 - Refereed conference paper (with host publication)peer-review

1 Scopus Citations
View graph of relations

Author(s)

  • Nicolas Privault

Related Research Unit(s)

Detail(s)

Original languageEnglish
Title of host publicationSeminaire de Probabilites XLI
Pages379-399
Volume1934
Publication statusPublished - 2008

Publication series

NameLecture Notes in Mathematics
Volume1934
ISSN (Print)0075-8434

Abstract

A probabilistic interpretation is constructed for the symmetry group G of the finite difference-differential equation ∂t η(x, t) = η(x, t) - η(x + 1, t) using the Doob transform for Markov (jump) processes. While the first three generators of G correspond to the identity and to space and time shifts, we show that in this interpretation the fourth generator of G is associated to time dilations and is linked to a creation operator on the Poisson space. © 2008 Springer-Verlag Berlin Heidelberg.

Research Area(s)

  • Doob transform, Finite difference equations, Jump processes, Symmetries

Citation Format(s)

A probabilistic interpretation to the symmetries of a discrete heat equation. / Privault, Nicolas.
Seminaire de Probabilites XLI. Vol. 1934 2008. p. 379-399 (Lecture Notes in Mathematics; Vol. 1934).

Research output: Chapters, Conference Papers, Creative and Literary WorksRGC 32 - Refereed conference paper (with host publication)peer-review