It is well known that the transition semigroup of an Ornstein Uhlenbeck process with delay is not strong Feller for small times, so it has no regularizing effects when acting on bounded and continuous functions. In this paper we study regularizing properties of this transition semigroup when acting on special functions of the past trajectory. With this regularizing property, we are able to prove existence and uniqueness of a mild solution for a special class of semilinear Kolmogorov equations; we apply these results to a stochastic optimal control problem.

Masiero, F., Tessitore, G. (2022). Partial smoothing of delay transition semigroups acting on special functions. JOURNAL OF DIFFERENTIAL EQUATIONS, 316(15 April 2022), 599-640 [10.1016/j.jde.2022.01.054].

Partial smoothing of delay transition semigroups acting on special functions

Masiero F.
;
Tessitore G.
2022

Abstract

It is well known that the transition semigroup of an Ornstein Uhlenbeck process with delay is not strong Feller for small times, so it has no regularizing effects when acting on bounded and continuous functions. In this paper we study regularizing properties of this transition semigroup when acting on special functions of the past trajectory. With this regularizing property, we are able to prove existence and uniqueness of a mild solution for a special class of semilinear Kolmogorov equations; we apply these results to a stochastic optimal control problem.
Articolo in rivista - Articolo scientifico
stochastic delay differerential equations; Ornstein-Uhlenbeck transition semigroups; partial smoothing properties;
English
599
640
42
Masiero, F., Tessitore, G. (2022). Partial smoothing of delay transition semigroups acting on special functions. JOURNAL OF DIFFERENTIAL EQUATIONS, 316(15 April 2022), 599-640 [10.1016/j.jde.2022.01.054].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/359711
Citazioni
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
Social impact