Convex Computation of Extremal Invariant Measures of Nonlinear Dynamical Systems and Markov Processes
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Nonlinear Science"
DOI: 10.1007/s00332-020-09658-1
Abstract: We propose a convex-optimization-based framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and continuous time. The set of all invariant measures is characterized as the feasible set of… read more here.
Keywords: computation; systems markov; measure; dynamical systems ... See more keywords
Existence of invariant measures for some damped stochastic dispersive equations
Sign Up to like & getrecommendations! Published in 2017 at "Comptes Rendus Mathematique"
DOI: 10.1016/j.crma.2017.04.018
Abstract: Abstract We address the long-time behavior of solutions to damped dispersive stochastic partial differential equations, namely the KdV equation and the nonlinear Schrodinger equation on the whole space. We prove that the transition semigroup is… read more here.
Keywords: existence; damped stochastic; measures damped; existence invariant ... See more keywords
Weak solutions and invariant measures of stochastic Oldroyd-B type model driven by jump noise
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2020.10.009
Abstract: Abstract In this work, we consider sub-critical and critical models for viscoelastic flows driven by pure jump Levy noise. Due to the elastic property, the noise in the equation for the stress tensor is considered… read more here.
Keywords: solutions invariant; stochastic oldroyd; weak solutions; model ... See more keywords
On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model
Sign Up to like & getrecommendations! Published in 2019 at "Physica A: Statistical Mechanics and its Applications"
DOI: 10.1016/j.physa.2019.04.181
Abstract: Abstract In this paper, we consider a stochastic epidemic model with time delay and general incidence rate. We first prove the existence and uniqueness of the global positive solution. By using the Krylov–Bogoliubov method, we… read more here.
Keywords: asymptotic behavior; epidemic model; measures asymptotic; invariant measures ... See more keywords
A strongly irreducible affine iterated function system with two invariant measures of maximal dimension
Sign Up to like & getrecommendations! Published in 2020 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2020.107
Abstract: Abstract A classical theorem of Hutchinson asserts that if an iterated function system acts on $\mathbb {R}^{d}$ by similitudes and satisfies the open set condition then it admits a unique self-similar measure with Hausdorff dimension… read more here.
Keywords: measures maximal; dimension; iterated function; invariant measures ... See more keywords
A scalable approach to the computation of invariant measures for high-dimensional Markovian systems
Sign Up to like & getrecommendations! Published in 2018 at "Scientific Reports"
DOI: 10.1038/s41598-018-19863-4
Abstract: The Markovian invariant measure is a central concept in many disciplines. Conventional numerical techniques for data-driven computation of invariant measures rely on estimation and further numerical processing of a transition matrix. Here we show how… read more here.
Keywords: high dimensional; transition; computation; computation invariant ... See more keywords
Supports of invariant measures for piecewise deterministic Markov processes
Sign Up to like & getrecommendations! Published in 2017 at "Nonlinearity"
DOI: 10.1088/1361-6544/aa7e94
Abstract: For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant control sets… read more here.
Keywords: supports invariant; piecewise deterministic; deterministic markov; markov processes ... See more keywords
Global martingale and pathwise solutions and infinite regularity of invariant measures for a stochastic modified Swift–Hohenberg equation
Sign Up to like & getrecommendations! Published in 2022 at "Nonlinearity"
DOI: 10.1088/1361-6544/acc6b1
Abstract: We consider a 2D stochastic modified Swift–Hohenberg equations with multiplicative noise and periodic boundary. First, we establish the existence of local and global martingale and pathwise solutions in the regular Sobolev space H2m for each… read more here.
Keywords: pathwise; invariant measures; modified swift; stochastic modified ... See more keywords
Lyapunov exponents and invariant measures on a projective bundle
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Notes"
DOI: 10.1134/s0001434617030245
Abstract: A discrete dynamical system generated by a diffeomorphism f on a compact manifold is considered. The Morse spectrum is the limit set of Lyapunov exponents of periodic pseudotrajectories. It is proved that the Morse spectrum… read more here.
Keywords: measures projective; projective bundle; exponents invariant; invariant measures ... See more keywords
On the Systems of Finite Weights on the Algebra of Bounded Operators and Corresponding Translation Invariant Measures
Sign Up to like & getrecommendations! Published in 2019 at "Lobachevskii Journal of Mathematics"
DOI: 10.1134/s1995080219080067
Abstract: We describe the class of translation invariant measures on the algebra ℬ(ℋ) of bounded linear operators on a Hilbert space ℋ and some of its subalgebras. In order to achieve this we apply two steps.… read more here.
Keywords: algebra bounded; translation invariant; translation; finite weights ... See more keywords