Abstract
We are concerned with backward Kolmogorov equations (both in the evolutionary and in the stationary version) associated with stochastic reaction-diffusion systems with additive noise in bounded domains of ℝd, with d ≤ 3. Our aim is proving that the transition semigroup corresponding to the stochastic system provides the unique classical solutions to the Kolmogorov problems.
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Cerrai, S. (2002). Classical Solutions for Kolmogorov Equations in Hilbert Spaces. 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_5
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DOI: https://doi.org/10.1007/978-3-0348-8209-5_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9474-6
Online ISBN: 978-3-0348-8209-5
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