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On an explicit representation of the solution of linear stochastic partial differential equations with delays

Abstract : Based on the analysis of a certain class of linear operators on a Banach space, we provide a closed form expression for the solutions of certain linear partial differential equations with non-autonomous input, time delays and stochastic terms, which takes the form of an infinite series expansion.
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https://hal.inria.fr/hal-00845589
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Submitted on : Wednesday, July 17, 2013 - 2:13:40 PM
Last modification on : Wednesday, July 21, 2021 - 3:48:34 AM

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Mathieu Galtier, Jonathan Touboul. On an explicit representation of the solution of linear stochastic partial differential equations with delays. Comptes Rendus. Mathématique, Centre Mersenne (2020-..) ; Elsevier Masson (2002-2019), 2012, 350 (3--4), pp.167 - 172. ⟨10.1016/j.crma.2012.01.004⟩. ⟨hal-00845589⟩

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