scholarly journals Existence of a unique invariant measure for a class of equicontinuous Markov operators with application to a stochastic model for an autoregulated gene

2016 ◽  
Vol 23 (2) ◽  
pp. 171-217 ◽  
Author(s):  
Sander Hille ◽  
Katarzyna Horbacz ◽  
Tomasz Szarek
Keyword(s):  
Invariant Measure ◽  
Stochastic Model ◽  
Markov Operators ◽  
Unique Invariant Measure

scholarly journals Markov operators with a unique invariant measure

2002 ◽  
Vol 276 (1) ◽  
pp. 343-356 ◽  
Author(s):  
Andrzej Lasota ◽  
Józef Myjak ◽  
Tomasz Szarek
Keyword(s):  
Invariant Measure ◽  
Markov Operators ◽  
Unique Invariant Measure

Invariant measure for the Vasicek interest rate model in the Heath–Jarrow–Morton–Musiela framework

2015 ◽  
Vol 18 (03) ◽  
pp. 1550022 ◽  
Author(s):  
Francesco Cordoni ◽  
Luca Di Persio
Keyword(s):  
Invariant Measure ◽  
Stochastic Partial Differential Equation ◽  
Forward Rate ◽  
Infinite Dimensional ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Unique Invariant Measure

In this paper we study a particular class of forward rate problems, related to the Vasicek model, where the driving equation is a linear Gaussian stochastic partial differential equation. We first give an existence and uniqueness results of the related mild solution in infinite dimensional setting, then we study the related Ornstein–Uhlenbeck semigroup with respect to the determination of a unique invariant measure for the associated Heath–Jarrow–Morton–Musiela model.

scholarly journals A classification of orbits admitting a unique invariant measure

2017 ◽  
Vol 168 (1) ◽  
pp. 19-36 ◽  
Author(s):  
Nathanael Ackerman ◽  
Cameron Freer ◽  
Aleksandra Kwiatkowska ◽  
Rehana Patel
Keyword(s):  
Invariant Measure ◽  
Unique Invariant Measure

scholarly journals Invariant measure of stochastic higher order KdV equation driven by Poisson processes

2021 ◽  
Author(s):  
Pengfei Xu ◽  
Jianhua Huang ◽  
Wei Yan
Keyword(s):  
Invariant Measure ◽  
Poisson Process ◽  
Initial Conditions ◽  
Kdv Equation ◽  
Higher Order ◽  
Poisson Processes ◽  
Current Paper ◽  
Well Posedness ◽  
Kdv Equations ◽  
Unique Invariant Measure

The current paper is devoted to stochastic damped KdV equations of higher order driven by Poisson process. We establish the well-posedness of stochastic damped higher-order KdV equations, and prove that there exists an unique invariant measure for deterministic initial conditions. Some discussion on the general pure jump noise case are also provided.

scholarly journals Exponential Convergence For Markov Systems

2015 ◽  
Vol 29 (1) ◽  
pp. 139-149 ◽  
Author(s):  
Maciej Ślęczka
Keyword(s):  
Invariant Measure ◽  
Exponential Convergence ◽  
Iterated Function Systems ◽  
Markov Systems ◽  
Markov Operators ◽  
Iterated Function

AbstractMarkov operators arising from graph directed constructions of iterated function systems are considered. Exponential convergence to an invariant measure is proved.

scholarly journals Dimensional characteristics of invariant measures for circle diffeomorphisms

2009 ◽  
Vol 29 (6) ◽  
pp. 1979-1992 ◽  
Author(s):  
VICTORIA SADOVSKAYA
Keyword(s):  
Invariant Measure ◽  
Rotation Number ◽  
Invariant Measures ◽  
Liouville Number ◽  
Hausdorff Dimensions ◽  
Rotation Numbers ◽  
Circle Diffeomorphism ◽  
Unique Invariant Measure ◽  
Circle Diffeomorphisms ◽  
Box Dimensions

AbstractWe consider pointwise, box, and Hausdorff dimensions of invariant measures for circle diffeomorphisms. We discuss the cases of rational, Diophantine, and Liouville rotation numbers. Our main result is that for any Liouville number τ there exists a C∞ circle diffeomorphism with rotation number τ such that the pointwise and box dimensions of its unique invariant measure do not exist. Moreover, the lower pointwise and lower box dimensions can equal any value 0≤β≤1.

ERGODICITY FOR THE PHASE-FIELD EQUATIONS PERTURBED BY GAUSSIAN NOISE

2011 ◽  
Vol 14 (01) ◽  
pp. 35-55 ◽  
Author(s):  
VIOREL BARBU ◽  
GIUSEPPE DA PRATO
Keyword(s):  
Invariant Measure ◽  
Phase Field ◽  
Gaussian Noise ◽  
Phase Field Model ◽  
Field Equations ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Phase Field Equations ◽  
Unique Invariant Measure ◽  
Von Neumann Theorem

We prove that the transition semigroup associated with the phase-field equations perturbed by a Gaussian noise has an invariant measure and it is irreducible and strong Feller. This implies by Doob's theorem that it possesses a unique invariant measure which is ergodic and strongly mixing. This implies the ergodicity of the flow associated with the phase-field model of phase transition in the sense of Birkhoff–von Neumann theorem. Such a result seems to be new in this context.

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