Branching processes for the fragmentation equation

DOI10.1016/j.spa.2014.11.016zbMath1310.60116OpenAlexW2030139938MaRDI QIDQ2018562

Madalina Deaconu, Lucian Beznea, Oana Lupaşcu

Publication date: 24 March 2015

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2014.11.016

zbMATH Keywords

stochastic differential equationbranching processesabsorbing setfragmentation equationmeasure-valued processexcessive functionbranching semigroup

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov semigroups and applications to diffusion processes (47D07) Probabilistic potential theory (60J45) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Transition functions, generators and resolvents (60J35) Right processes (60J40)

Related Items

Measure-valued branching processes associated with Neumann nonlinear semiflows, Stochastic equation of fragmentation and branching processes related to avalanches, Numerical solution for the non-linear Dirichlet problem of a branching process, Probabilistic representations of fragmentation equations, Numerical approach for stochastic differential equations of fragmentation; application to avalanches, Measure-valued discrete branching Markov processes, Random multiple-fragmentation and flow of particles on a surface, From Gaussian estimates for nonlinear evolution equations to the long time behavior of branching processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Applications of compact superharmonic functions: path regularity and tightness of capacities
• Glauber dynamics in the continuum via generating functionals evolution
• Strong fragmentation and coagulation with power-law rates
• Calcul stochastique et problèmes de martingales
• Nonlinear PDEs and measure-valued branching type processes
• From resolvents to càdlàg processes through compact excessive functions and applications to singular SDE on Hilbert spaces
• Uniqueness via probabilistic interpretation for the discrete coagulation fragmentation equation
• Quasi-regular Dirichlet forms and \(L^p\)-resolvents on measurable spaces
• Markov processes associated with \(L^{p}\)-resolvents and applications to stochastic differential equations on Hilbert space
• Asymptotic behavior of solutions of the fragmentation equation with shattering: an approach via self-similar Markov processes
• Construction and regularity of measure-valued Markov branching processes
• Smoluchowski's coagulation equation: Uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent
• Feyel's techniques on the supermedian functionals and strongly supermedian functions
• Fine densities for excessive measures and the Revuz correspondence
• Self-similar fragmentations
• On self-similarity and stationary problem for fragmentation and coagulation models.
• On small particles in coagulation-fragmentation equations
• A pure jump Markov process associated with Smoluchowski's coagulation equation
• Projective limits of probability spaces
• 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
• Branching Markov processes. I
• Branching Markov processes. III
• Probabilistic approach of some discrete and continuous coagulation equations with diffusion.
• Loss of mass in deterministic and random fragmentations.
• Global strict solutions to continuous coagulation–fragmentation equations with strong fragmentation
• Measure-Valued Branching Markov Processes
• Inverse Limits of Measure Spaces
• On Bochner-Kolmogorov Theorem
• Existence and uniqueness results for the continuous coagulation and fragmentation equation
• Random Fragmentation and Coagulation Processes
• Markov processes with creation of particles
• Homogeneous fragmentation processes