On transformations of smooth measure related to parabolic and hyperbolic differential equations in infinite dimensions

Yu Daletskii; Victoria Steblovskaya

On transformations of smooth measure related to parabolic and hyperbolic differential equations in infinite dimensions

Yu Daletskii
, Victoria Steblovskaya

Mathematical Sciences

Research output: Contribution to journal › Article

Abstract

We consider an evolution μ → μ_t of a smooth measure μ related to parabolic and hyperbolic differential equations in infinite dimensions. In both cases conditions under which the initial measure is invariant with respect to corresponding evolution are given. For the case of parabolic equation we obtain conditions of the absolute continuity μ_t ≺ μ and a formula for the density μ_t(dcursive Greek chi)/μ(dcursive Greek chi).

Original language	English
Pages (from-to)	989-1007
Journal	Stochastic Analysis and Applications
Volume	16
Issue number	5
State	Published - 1998

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title = "On transformations of smooth measure related to parabolic and hyperbolic differential equations in infinite dimensions",

abstract = "We consider an evolution μ → μt of a smooth measure μ related to parabolic and hyperbolic differential equations in infinite dimensions. In both cases conditions under which the initial measure is invariant with respect to corresponding evolution are given. For the case of parabolic equation we obtain conditions of the absolute continuity μt ≺ μ and a formula for the density μt(dcursive Greek chi)/μ(dcursive Greek chi).",

author = "Yu Daletskii and Victoria Steblovskaya",

year = "1998",

language = "English",

volume = "16",

pages = "989--1007",

journal = "Stochastic Analysis and Applications",

number = "5",

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TY - JOUR

T1 - On transformations of smooth measure related to parabolic and hyperbolic differential equations in infinite dimensions

AU - Daletskii, Yu

AU - Steblovskaya, Victoria

PY - 1998

Y1 - 1998

N2 - We consider an evolution μ → μt of a smooth measure μ related to parabolic and hyperbolic differential equations in infinite dimensions. In both cases conditions under which the initial measure is invariant with respect to corresponding evolution are given. For the case of parabolic equation we obtain conditions of the absolute continuity μt ≺ μ and a formula for the density μt(dcursive Greek chi)/μ(dcursive Greek chi).

AB - We consider an evolution μ → μt of a smooth measure μ related to parabolic and hyperbolic differential equations in infinite dimensions. In both cases conditions under which the initial measure is invariant with respect to corresponding evolution are given. For the case of parabolic equation we obtain conditions of the absolute continuity μt ≺ μ and a formula for the density μt(dcursive Greek chi)/μ(dcursive Greek chi).

M3 - Article

VL - 16

SP - 989

EP - 1007

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 5

ER -

On transformations of smooth measure related to parabolic and hyperbolic differential equations in infinite dimensions

Abstract

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