A probabilistic interpretation to the symmetries of a discrete heat equation
Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review
Author(s)
Related Research Unit(s)
Detail(s)
Original language | English |
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Title of host publication | Seminaire de Probabilites XLI |
Pages | 379-399 |
Volume | 1934 |
Publication status | Published - 2008 |
Publication series
Name | Lecture Notes in Mathematics |
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Volume | 1934 |
ISSN (Print) | 0075-8434 |
Link(s)
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).
Seminaire de Probabilites XLI. Vol. 1934 2008. p. 379-399 (Lecture Notes in Mathematics; Vol. 1934).
Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review