scholarly journals Existence and uniqueness of invariant measures for a class of transition semigroups on Hilbert spaces

2009 ◽  
Vol 353 (2) ◽  
pp. 497-507 ◽  
Author(s):  
Abdelhadi Es-Sarhir
Keyword(s):  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Invariant Measures ◽  
Transition Semigroups

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

scholarly journals On invariant measures of nonlinear Markov processes

1993 ◽  
Vol 6 (4) ◽  
pp. 385-406 ◽  
Author(s):  
N. U. Ahmed ◽  
Xinhong Ding
Keyword(s):  
Markov Process ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Invariant Measures ◽  
Nonlinear Markov Processes

We consider a nonlinear (in the sense of McKean) Markov process described by a stochastic differential equations in Rd. We prove the existence and uniqueness of invariant measures of such process.

scholarly journals Convergence and stability of the three-step iterative schemes for a class of general quasivariational-like inequalities

2004 ◽  
Vol 2004 (70) ◽  
pp. 3849-3857
Author(s):  
Zeqing Liu ◽  
Zhefu An ◽  
Shin Min Kang ◽  
Jeong Sheok Ume
Keyword(s):  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Iterative Schemes ◽  
Convergence And Stability

We introduce and study a class of general quasivariational-like inequalities in Hilbert spaces, suggest two general algorithms, and establish the existence and uniqueness of solutions for these kinds of inequalities. Under certain conditions, we discuss convergence and stability of the three-step iterative sequences generated by the algorithms.

Conditionally invariant measures for Anosov maps with small holes

1998 ◽  
Vol 18 (5) ◽  
pp. 1049-1073 ◽  
Author(s):  
N. CHERNOV ◽  
R. MARKARIAN ◽  
S. TROUBETZKOY
Keyword(s):  
Invariant Measure ◽  
Existence And Uniqueness ◽  
Invariant Measures ◽  
Smooth Boundary ◽  
Piecewise Smooth ◽  
Piecewise Smooth Boundary ◽  
Conditional Distributions ◽  
The Past ◽  
Set Of Points ◽  
Small Holes

We study Anosov diffeomorphisms on surfaces in which some small ‘holes’ are cut. The points that are mapped into those holes disappear and never return. We assume that the holes are arbitrary open domains with piecewise smooth boundary, and their sizes are small enough. The set of points whose trajectories never enter holes under the past iterations of the map is a Cantor-like union of unstable fibers. We establish the existence and uniqueness of a conditionally invariant measure on this set, whose conditional distributions on unstable fibers are smooth. This generalizes previous works by Pianigiani, Yorke, and others.

On the norm continuity of transition semigroups in Hilbert spaces

1998 ◽  
Vol 70 (1) ◽  
pp. 52-56 ◽  
Author(s):  
Wolfgang Desch ◽  
Abdelaziz Rhandi
Keyword(s):  
Hilbert Spaces ◽  
Norm Continuity ◽  
Transition Semigroups

A SIMILARITY BETWEEN THE GROSS LAPLACIAN AND THE LÉVY LAPLACIAN

2007 ◽  
Vol 10 (02) ◽  
pp. 261-276 ◽  
Author(s):  
UN CIG JI ◽  
KIMIAKI SAITÔ
Keyword(s):  
Stochastic Process ◽  
Hilbert Space ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Infinitesimal Generator ◽  
Separable Hilbert Space ◽  
Fock Spaces ◽  
Parameter Group ◽  
Infinite Dimensional ◽  
Lévy Laplacian

In this paper we present a construction of an infinite dimensional separable Hilbert space associated with a norm induced from the Lévy trace. The space is slightly different from the Cesàro Hilbert space introduced in Ref. 1. The Lévy Laplacian is discussed with a suitable domain which is constructed by a rigging of Fock spaces based on a rigging of Hilbert spaces with the Lévy trace. Then the Lévy Laplacian can be considered as the Gross Laplacian acting on a certain countable Hilbert space. By constructing one-parameter group of operators of which the infinitesimal generator is the Lévy Laplacian, we study the existence and uniqueness of solution of heat equation associated with the Lévy Laplacian. Moreover we give an infinite dimensional stochastic process generated by the Lévy Laplacian.

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