Nonlinear parabolic P.D.E. and additive functionals of superdiffusions

DOI10.1214/aop/1024404415zbMath0880.60080OpenAlexW2006465630MaRDI QIDQ1356360

S. E. Kuznetsov, E. B. Dynkin

Publication date: 3 February 1998

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1024404415

zbMATH Keywords

polar setsbranchingpotentialscapacitiesmeasure-valued processesboundary value problems involving measureslog-potentialsnatural linear additive functionalsprobabilistic solutions of partial differential equations

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Diffusion processes (60J60) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Potentials and capacities on other spaces (31C15) Local time and additive functionals (60J55) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items

Natural linear additive functionals of superprocesses, Backward stochastic differential equations with singular terminal condition, Stochastic boundary values and boundary singularities for solutions of the equation \(Lu=u^\alpha\), Stochastic partial differential equations with singular terminal condition, Semilinear parabolic equations, diffusions, and superdiffusions, Removable lateral singularities of semilinear parabolic PDEs and Besov capacities, Semilinear parabolic equations with measure boundary data and isolated singularities, Integro-partial differential equations with singular terminal condition

Cites Work

• Superprocesses and partial differential equations
• A weighted occupation time for a class of measure-valued branching processes
• Path processes and historical superprocesses
• Branching particle systems and superprocesses
• Singularités éliminables pour des équations semi-linéaires
• Construction and regularity of measure-valued Markov branching processes
• Boundary singularities of solutions of some nonlinear elliptic equations
• Superdiffusion and parabolic nonlinear differential equations
• Sufficient statistics and extreme points
• On regularity of superprocesses
• Natural linear additive functionals of superprocesses
• The Brownian snake and solutions of \(\Delta u = u^ 2\) in a domain
• Solutions of \(Lu = u^ \alpha\) dominated by \(L\)-harmonic functions
• Problems paraboliques semi-lineaires avec donnees measures
• Superprocesses and their Linear Additive Functionals
• Construction of Markov Processes with Random Times of Birth and Death
• An Introduction to Branching Measure-Valued Processes
• Superdiffusions and removable singularities for quasilinear partial differential equations
• Linear additive functionals of superdiffusions and related nonlinear P.D.E.
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