Cauchy problem for nonautonomous Kolmogorov equations

Guiotto, Paolo

doi:10.1080/07362999608809447

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2006

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“…and that there exists a unique mild solution of (1.1) (see e.g. [5]). We define the transition evolution operator REMARK 1.2.…”

Section: Introductionmentioning

confidence: 99%

Dissipative stochastic equations in Hilbert space with time dependent coefficients

Prato¹,

Röckner²

2006

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.

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We prove existence and, under an additional assumption, uniqueness of an evolution system of measures (ν t ) t∈R for a stochastic differential equation with time dependent dissipative coefficients. We prove that if P s,t denotes the corresponding transition evolution operator, then P s,t ϕ behaves asymptotically as t → +∞ like a limit curve (which is independent of s) for any continuous and bounded "observable" ϕ.

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“…and that there exists a unique mild solution of (1.1) (see e.g. [5]). We define the transition evolution operator REMARK 1.2.…”

Section: Introductionmentioning

confidence: 99%

Dissipative stochastic equations in Hilbert space with time dependent coefficients

Prato¹,

Röckner²

2006

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.

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Cauchy problem for nonautonomous Kolmogorov equations

Abstract: We study the existence and uniqueness of the strict solutions of an initial value problem for a nonautonomous Kolmogorov equation in a space of unbounded functions

Cited by 1 publication

References 9 publications

Dissipative stochastic equations in Hilbert space with time dependent coefficients

Dissipative stochastic equations in Hilbert space with time dependent coefficients

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