JournalsrlmVol. 17, No. 4pp. 397–403

Dissipative stochastic equations in Hilbert space with time dependent coefficients

  • Michael Röckner

    Purdue University, West Lafayette, USA
  • Giuseppe Da Prato

    Scuola Normale Superiore, Pisa, Italy
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Abstract

We prove existence and, under an additional assumption, uniqueness of an evolution system of measures (νt)tR(\nu_t)_{t\in \R} for a stochastic differential equation with time dependent dissipative coefficients. We prove that if Ps,tP_{s,t} denotes the corresponding transition evolution operator, then Ps,tφP_{s,t}\varphi behaves asymptotically as t+t\to +\infty like a limit curve (which is independent of ss) for any continuous and bounded ``observable'' φ\varphi.

Cite this article

Michael Röckner, Giuseppe Da Prato, Dissipative stochastic equations in Hilbert space with time dependent coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 4, pp. 397–403

DOI 10.4171/RLM/476