Abstract
The aim of the paper is to prove some significative results for a given class of stochastic evolution equations by means of a suitable adaptation of techniques (the stochastic characteristics method and a Itô-type formula for backward diffusions) which are already known in the literature, but not so widely used.
We are able to prove both the existence of a stochastic flow related to the equation in spaces of continuous functions and a representation formula for the solution of the equation.
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Bonaccorsi, S., Guatteri, G. (2002). Classical Solutions for SPDEs with Dirichlet Boundary Conditions. In: Dalang, R.C., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications III. Progress in Probability, vol 52. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8209-5_3
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DOI: https://doi.org/10.1007/978-3-0348-8209-5_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9474-6
Online ISBN: 978-3-0348-8209-5
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