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.
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Privault, N. (2008). A probabilistic interpretation to the symmetries of a discrete heat equation. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLI. Lecture Notes in Mathematics, vol 1934. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77913-1_18
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DOI: https://doi.org/10.1007/978-3-540-77913-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77912-4
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