16 results match your criteria markov semigroups

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Invariant Measures for the Stochastic One-Dimensional Compressible Navier-Stokes Equations.

Appl Math Optim 2021 16;83(3):1487-1522. Epub 2019 Jul 16.

Department of Mathematics, University of Maryland, College Park, MD 20742 USA.

We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an invariant measure for the Markov process generated by strong solutions. We overcome the difficulties of working with non-Feller Markov semigroups on non-complete metric spaces by generalizing the classical Krylov-Bogoliubov method, and by providing suitable polynomial and exponential moment bounds on the solution, together with pathwise estimates. Read More

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Complete Gradient Estimates of Quantum Markov Semigroups.

Commun Math Phys 2021 30;387(2):761-791. Epub 2021 Aug 30.

Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria.

In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors. Read More

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Analytic solutions for stochastic hybrid models of gene regulatory networks.

J Math Biol 2021 01 26;82(1-2). Epub 2021 Jan 26.

Computer Science Department, Saarland University, 66123, Saarbrücken, Germany.

Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely large. Therefore hybrid models, in which protein counts are replaced by average protein concentrations, have become a popular alternative. Read More

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January 2021

A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching.

J Franklin Inst 2019 Nov 13;356(16):9844-9866. Epub 2019 Sep 13.

School of Science, Jimei University, Xiamen, China.

In this paper, we propose and discuss a stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. First of all, we show that there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by the basic reproduction number is established: the disease can be eradicated almost surely if and under mild extra conditions, whereas if the densities of the distributions of the solution can converge in to an invariant density by using the Markov semigroups theory. Read More

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November 2019

Dynamics of a nutrient-phytoplankton model with random phytoplankton mortality.

J Theor Biol 2020 03 19;488:110119. Epub 2019 Dec 19.

School of Mathematical Science, Huaiyin Normal University, 111 West Changjiang Road, Huaian, Jiangsu 223300, PR China.

This study formulates a stochastic nutrient-phytoplankton model which incorporates the effect of white noise on phytoplankton growth. The global existence and uniqueness of a positive solution, stochastic boundedness, and stochastically asymptotic stability are well explored. A stochastic ecological reproductive index R is formulated to characterize the global dynamics. Read More

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A model of HBV infection with intervention strategies: dynamics analysis and numerical simulations.

Math Biosci Eng 2019 03;16(4):2562-2586

School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, P.R. China.

In this paper, we analyze the effect of environment noise on the transmission dynamics of a stochastic hepatitis B virus (HBV) infection model with intervention strategies. By using the Markov semigroups theory, we define the stochastic basic reproduction number and find it can be used to govern disease extinction or persistence. When it is less than one, under a mild extra condition, the stochastic system has a disease-free equilibrium and the disease is predicted to die out with probability one. Read More

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Lie-Markov Models Derived from Finite Semigroups.

Bull Math Biol 2019 02 2;81(2):361-383. Epub 2018 Aug 2.

School of Physical Sciences, University of Tasmania, Hobart, Australia.

We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is k, the resulting model is a continuous-time Markov chain on k-states and, as a consequence of the product rule in the semigroup, satisfies the property of multiplicative closure. This means that the product of any two probability substitution matrices taken from the model produces another substitution matrix also in the model. Read More

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February 2019

Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations.

Math Biosci Eng 2017 Oct/Dec 1;14(5-6):1477-1498

Lamps and Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada

In this paper, we investigate the dynamics of a delayed logistic model with both impulsive and stochastic perturbations. The impulse is introduced at fixed moments and the stochastic perturbation is of white noise type which is assumed to be proportional to the population density. We start with the existence and uniqueness of the positive solution of the model, then establish sufficient conditions ensuring its global attractivity. Read More

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Mathematical model of stem cell differentiation and tissue regeneration with stochastic noise.

Bull Math Biol 2014 Jul 18;76(7):1642-69. Epub 2014 Jul 18.

Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland,

Differentiation and self-renewal of stem cells is an essential process for the maintenance of tissue composition. The promise of novel medical therapies combined with the complexity of this process encourage us to employ numerical and mathematical methods. This will allow us to understand better the mechanisms which regulate stem cell behaviour. Read More

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Kolmogorov's differential equations and positive semigroups on first moment sequence spaces.

J Math Biol 2006 Oct 28;53(4):642-71. Epub 2006 Apr 28.

Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611-8105, USA.

Spatially implicit metapopulation models with discrete patch-size structure and host-macroparasite models which distinguish hosts by their parasite loads lead to infinite systems of ordinary differential equations. In several papers, a this-related theory will be developed in sufficient generality to cover these applications. In this paper the linear foundations are laid. Read More

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October 2006

Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps.

Proc Natl Acad Sci U S A 2005 May 17;102(21):7426-31. Epub 2005 May 17.

Department of Mathematics, Program in Applied Mathematics, Yale University, New Haven, CT 06510, USA.

We provide a framework for structural multiscale geometric organization of graphs and subsets of R(n). We use diffusion semigroups to generate multiscale geometries in order to organize and represent complex structures. We show that appropriately selected eigenfunctions or scaling functions of Markov matrices, which describe local transitions, lead to macroscopic descriptions at different scales. Read More

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Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods.

Proc Natl Acad Sci U S A 2005 May 17;102(21):7432-7. Epub 2005 May 17.

Department of Mathematics, Program in Applied Mathematics, Yale University, New Haven, CT 06510, USA.

In the companion article, a framework for structural multiscale geometric organization of subsets of R(n) and of graphs was introduced. Here, diffusion semigroups are used to generate multiscale analyses in order to organize and represent complex structures. We emphasize the multiscale nature of these problems and build scaling functions of Markov matrices (describing local transitions) that lead to macroscopic descriptions at different scales. Read More

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Diffusion processes, Feller semigroups and Wentzell boundary conditions.

Authors:
S Romanelli

Riv Biol 2001 May-Aug;94(2):319-25

Dipartimento di Matematica, Università di Bari, Via E. Orabona 4, 70125 Bari.

Different approaches to the study of many diffusion processes in Genetics involve Probability, Functional Analysis and Partial Differential Equations, as in the case of changes in gene frequency due only to random sampling or under random fluctuation of selective advantages. In the one-dimensional case, a unified treatment of them was given by Feller. For particular classes of Markov processes, Taira showed that these different approaches are equivalent even in the N-dimensional case. Read More

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December 2001

Skewed base compositions, asymmetric transition matrices, and phylogenetic invariants.

J Comput Biol 1994 ;1(1):77-92

Université de Montréal, CRM, Montreal, Quebec, Canada.

Evolutionary inference methods that assume equal DNA base compositions and symmetric nucleotide substitution matrices, where these assumptions do not hold, are likely to group species on the basis of similar base compositions rather than true phylogenetic relationships. We propose an invariants-based method for dealing with this problem. An invariant QT of a tree T under a k-state Markov model, where a generalized time parameter is identified with the E edges of T, allows us to recognize whether data on N observed species can be associated with the N terminal vertices of T in the sense of having been generated on T rather than on any other tree with N terminals. Read More

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October 1996

Mechanized derivation of linear invariants.

Authors:
J A Cavender

Mol Biol Evol 1989 May;6(3):301-16

Department of Mathematics, University of Colorado, Denver 80204.

Linear invariants, discovered by Lake, promise to provide a versatile way of inferring phylogenies on the basis of nucleic acid sequences (the method that he called "evolutionary parsimony"). A semigroup of Markov transition matrices embodies the assumptions underlying the method, and alternative semigroups exist. The set of all linear invariants may be derived from the semigroup by using an algorithm described here. Read More

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From deterministic dynamics to probabilistic descriptions.

Proc Natl Acad Sci U S A 1979 Aug;76(8):3607-11

Faculté des Sciences Université Libre de Bruxelles, Campus Plaine, Boulevard du Triomphe, 1050 Bruxelles, Belgium.

THE PRESENT WORK IS DEVOTED TO THE FOLLOWING QUESTION: What is the relationship between the deterministic laws of dynamics and probabilistic description of physical processes? It is generally accepted that probabilistic processes can arise from deterministic dynamics only through a process of "coarse graining" or "contraction of description" that inevitably involves a loss of information. In this work we present an alternative point of view toward the relationship between deterministic dynamics and probabilistic descriptions. Speaking in general terms, we demonstrate the possibility of obtaining (stochastic) Markov processes from deterministic dynamics simply through a "change of representation" that involves no loss of information provided the dynamical system under consideration has a suitably high degree of instability of motion. Read More

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