Stochastic solutions to evolution equations of non-local branching processes

DOI10.1016/j.na.2020.112021zbMath1460.60093OpenAlexW3036444282MaRDI QIDQ2201749

Cătălin Ioan Vrabie, Oana Lupaşcu-Stamate, Lucian Beznea

Publication date: 17 September 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2020.112021

zbMATH Keywords

nonlinear evolution equationcontinuous additive functionalmeasure-valued processexcessive functionkilled processbranching semigroupnon-local branching processcompact Lyapunov function

Mathematics Subject Classification ID

Markov semigroups and applications to diffusion processes (47D07) Nonlinear elliptic equations (35J60) Probabilistic potential theory (60J45) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Superprocesses (60J68)

Related Items

\(h\)-transform of Doob and nonlocal branching processes, Random multiple-fragmentation and flow of particles on a surface, Evolution of states of an infinite particle system with nonlocal branching, Continuous flows driving branching processes and their nonlinear evolution equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Measure-valued branching processes associated with Neumann nonlinear semiflows
• Applications of compact superharmonic functions: path regularity and tightness of capacities
• Glauber dynamics in the continuum via generating functionals evolution
• Dirichlet forms and symmetric Markov processes.
• Nonlinear PDEs and measure-valued branching type processes
• On the quasi-regularity of non-sectorial Dirichlet forms by processes having the same polar sets
• From resolvents to càdlàg processes through compact excessive functions and applications to singular SDE on Hilbert spaces
• Branching particle systems and superprocesses
• Markov processes associated with \(L^{p}\)-resolvents and applications to stochastic differential equations on Hilbert space
• Feynman-Kac formula for left continuous additive functionals and extended Kato class measures
• Construction and regularity of measure-valued Markov branching processes
• Propriétés de martingales, explosion et représentation de Lévy- Khintchine d'une classe de processus de branchement à valeurs mesures. (Martingale properties, explosions and Levy-Khinchine representation of measure valued branching processes)
• Markov processes: Ray processes and right processes
• Measure perturbations of Markovian semigroups
• Continuous dependence of a class of superprocesses on branching parameters and applications
• Additive functionals, nowhere Radon and Kato class smooth measures associated with Dirichlet forms
• Nonlocal branching superprocesses and some related models
• An extended generator and Schrödinger equations
• From Gaussian estimates for nonlinear evolution equations to the long time behavior of branching processes
• Potential-theoretical methods in the construction of measure-valued Markov branching processes
• Bounded and \(L^p\)-weak solutions for nonlinear equations of measure-valued branching processes
• The explosion problem for branching Markov process
• Multi-dimensional diffusion and the Markov process on the boundary
• Branching Markov processes. I
• CONSTRUCTION OF SUPER-BROWNIAN MOTIONS
• Measure-valued discrete branching Markov processes
• Measure-Valued Branching Markov Processes
• An Introduction to Branching Measure-Valued Processes
• An Introduction to the Theory of Point Processes
• Markov processes with creation of particles
• Branching process associated with 2D-Navier-Stokes equation
• Measures not charging polar sets and Schrödinger equations in \(L^p\)