Stochastic Optimal Control in Infinite Dimension by Giorgio Fabbri Fausto Gozzi & Andrzej Święch

Author:Giorgio Fabbri, Fausto Gozzi & Andrzej Święch
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Here we present a result which only deals with the first case. The second case is more difficult and strongly dependent on a specific problem. Up to now it has only been studied in the specific case of reaction-diffusion equations (see [103, 105, 107] and also [106], Chaps. 9 and 10) which is presented briefly in Sect. 4.9.2.

We will need additional assumptions about the transition semigroup.

Hypothesis 4.133

Let and let be from Hypothesis 4.72 (and hence also Hypothesis 4.127).

(i)For all , and all , , the function

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