We prove uniqueness in law for possibly degenerate SDEs having a linear part in the drift term. Diffusion coefficients corresponding to non-degenerate directions of the noise are assumed to be continuous. When the diffusion part is constant we recover the classical degenerate Ornstein-Uhlenbeck process which only has to satisfy the Hörmander hypoellipticity condition. In the proof we also use global Lp-estimates for hypoelliptic Ornstein-Uhlenbeck operators recently proved in Bramanti et al. (Math. Z. 266, 789–816 2010) and adapt the localization procedure introduced by Stroock and Varadhan. Appendix contains a quite general localization principle for martingale problems.

On weak uniqueness for some degenerate SDEs by global Lp estimates

PRIOLA, Enrico
2015-01-01

Abstract

We prove uniqueness in law for possibly degenerate SDEs having a linear part in the drift term. Diffusion coefficients corresponding to non-degenerate directions of the noise are assumed to be continuous. When the diffusion part is constant we recover the classical degenerate Ornstein-Uhlenbeck process which only has to satisfy the Hörmander hypoellipticity condition. In the proof we also use global Lp-estimates for hypoelliptic Ornstein-Uhlenbeck operators recently proved in Bramanti et al. (Math. Z. 266, 789–816 2010) and adapt the localization procedure introduced by Stroock and Varadhan. Appendix contains a quite general localization principle for martingale problems.
2015
42
247
281
http://arxiv.org/pdf/1305.7174v3.pdf
Degenerate stochastic differential equations, Localization principle, Ornstein-Uhlenbeck processes, Well-posedness of martingale problem
Enrico Priola
File in questo prodotto:
File Dimensione Formato  
PotaPriolaarxiv2014.pdf

Accesso riservato

Tipo di file: PREPRINT (PRIMA BOZZA)
Dimensione 393.87 kB
Formato Adobe PDF
393.87 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/2318/150085
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 14
social impact