Markov evolutions and hierarchical equations in the continuum I. One-component systems

Abstract

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.

47 pages

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• Regulation mechanisms in spatial stochastic development models
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Cited by in corpus (30)

• Markov evolutions and hierarchical equations in the continuum I. One-component systems
• Vlasov scaling for stochastic dynamics of continuous systems
• Metric properties of discrete time exclusion type processes in continuum
• The statistical dynamics of a spatial logistic model and the related kinetic equation
• Glauber dynamics in the continuum via generating functionals evolution
• Markov evolutions and hierarchical equations in the continuum: II. Multicomponent systems
• Regulation mechanisms in spatial stochastic development models
• Operator approach to Vlasov scaling for some models of spatial ecology
• Traveling waves and long-time behavior in a doubly nonlocal Fisher-KPP equation
• On an aggregation in birth-and-death stochastic dynamics
• Non-equilibrium dynamics for a Widom-Rowlinson type model with mutations
• Functional evolutions for homogeneous stationary death-immigration spatial dynamics
• Glauber Dynamics in Continuum: A Constructive Approach to Evolution of States
• Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit
• Binary jumps in continuum. I. Equilibrium processes and their scaling limits
• Linear evolution equations in scales of Banach spaces
• Statistical dynamics of continuous systems: perturbative and approximative approaches
• Stochastic averaging principle for spatial Markov evolutions in the continuum
• Vlasov scaling for the Glauber dynamics in continuum
• A Markov process for an infinite interacting particle system in the continuum
• The Microscopic Dynamics of a Spatial Ecological Model
• Around Ovsyannikov's method
• Fractional contact model in the continuum
• Nonlinear perturbations of evolution systems in scales of Banach spaces
• Weak-coupling limit for ergodic environments
• Hydrodynamic limits for the free Kawasaki dynamics of continuous particle systems
• Infinite populations of migrants as complex systems: self-regulation
• General contact processes: inhomogeneous models, models on graphs and on manifolds
• Individual based model with competition in spatial ecology
• A Widom-Rowlinson Jump Dynamics in the Continuum