In this paper we study an Ergodic Markovian BSDE involving a forward process X that solves an infinite dimensional forward stochastic evolution equation with multiplicative and possibly degenerate diffusion coefficient. A concavity assumption on the driver allows us to avoid the typical quantitative conditions relating the dissipativity of the forward equation and the Lipschitz constant of the driver. Although the degeneracy of the noise has to be of a suitable type, we can give a stochastic representation of a large class of Ergodic HJB equations; moreover, our general results can be applied to achieve the synthesis of the optimal feedback law in relevant examples of ergodic control problems for SPDEs.

Guatteri, G., Tessitore, G. (2020). Ergodic BSDEs with multiplicative and degenerate noise. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 58(4), 2050-2077 [10.1137/19M1292552].

Ergodic BSDEs with multiplicative and degenerate noise

Tessitore G.
2020

Abstract

In this paper we study an Ergodic Markovian BSDE involving a forward process X that solves an infinite dimensional forward stochastic evolution equation with multiplicative and possibly degenerate diffusion coefficient. A concavity assumption on the driver allows us to avoid the typical quantitative conditions relating the dissipativity of the forward equation and the Lipschitz constant of the driver. Although the degeneracy of the noise has to be of a suitable type, we can give a stochastic representation of a large class of Ergodic HJB equations; moreover, our general results can be applied to achieve the synthesis of the optimal feedback law in relevant examples of ergodic control problems for SPDEs.
Articolo in rivista - Articolo scientifico
BSDEs; Ergodic control; Infinite dimensional SDEs; Multiplicative noise;
English
2020
58
4
2050
2077
none
Guatteri, G., Tessitore, G. (2020). Ergodic BSDEs with multiplicative and degenerate noise. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 58(4), 2050-2077 [10.1137/19M1292552].
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/10281/289271
Citazioni
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
Social impact