Functional evolutions for homogeneous stationary death-immigration spatial dynamics

Abstract

We discover death-immigration non-equilibrium stochastic dynamics in the continuum also known as the Surgailis process. Explicit expression for the correlation functions is presented. Dynamics of states and their generating functionals are studied. Ergodic properties for the evolutions are considered.

References in corpus (5)

• Spatial birth and death processes as solutions of stochastic equations
• Existence and spatial limit theorems for lattice and continuum particle systems
• Non-equilibrium stochastic dynamics in continuum: The free case
• An approximative approach to construction of the Glauber dynamics in continuum
• Correlation functions evolution for the Glauber dynamics in continuum

Cited by in corpus (5)

• On an aggregation in birth-and-death stochastic dynamics
• Non-equilibrium dynamics for a Widom-Rowlinson type model with mutations
• Linear evolution equations in scales of Banach spaces
• Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum
• Stochastic averaging for a spatial population model in random environment