Super-Brownian motion as the unique strong solution to an SPDE

DOI10.1214/12-AOP789zbMath1266.60119arXiv1203.4873MaRDI QIDQ1951698

Jie Xiong

Publication date: 24 May 2013

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

Full work available at URL: https://arxiv.org/abs/1203.4873

zbMATH Keywords

Fleming-Viot processstochastic partial differential equationbackward doubly stochastic differential equationstrong uniquenesssuper Brownian motion

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Superprocesses (60J68)

Related Items

Well-posedness of the martingale problem for superprocess with interaction, Backward doubly stochastic equations with jumps and comparison theorems, Central limit theorem for a class of SPDEs, On the convergence rates of some adaptive Markov chain Monte Carlo algorithms, Superprocesses with interaction and immigration, Uniqueness problem for SPDEs from population models, A distribution-function-valued SPDE and its applications, On the pathwise uniqueness of stochastic partial differential equations with non-Lipschitz coefficients, \(L_p\)-regularity theory for semilinear stochastic partial differential equations with multiplicative white noise, Strong existence and uniqueness to a class of nonlinear SPDEs driven by Gaussian colored noises, Backward doubly stochastic Volterra integral equations and their applications, A regularity theory for stochastic generalized Burgers' equation driven by a multiplicative space-time white noise, Long-time behavior for subcritical measure-valued branching processes with immigration, Forward-backward doubly stochastic systems and classical solutions of path-dependent stochastic PDEs, Well-posedness of the martingale problem for super-Brownian motion with interactive branching, On mean-field super-Brownian motions, Boundary behavior and interior Hölder regularity of the solution to nonlinear stochastic partial differential equation driven by space-time white noise, Strong uniqueness for an SPDE via backward doubly stochastic differential equations, Stochastic equations of super-Lévy processes with general branching mechanism, Large deviations under a viewpoint of metric geometry: measure-valued process cases, The reversibility and an SPDE for the generalized Fleming-Viot processes with mutation, Large deviation principle for some measure-valued processes, A regularity theory for stochastic partial differential equations with a super-linear diffusion coefficient and a spatially homogeneous colored noise, Existence and pathwise uniqueness to an SPDE driven by \(\alpha\)-stable colored noise, Moderate deviation principle for a class of stochastic partial differential equations, The law of the iterated logarithm for a class of SPDEs, Stochastic partial differential equations with gradient driven by space-time fractional noises, A regularity theory for stochastic partial differential equations driven by multiplicative space-time white noise with the random fractional Laplacians, Mutually interacting superprocesses with migration

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Well-posedness of the martingale problem for superprocess with interaction
• Stochastic equations, flows and measure-valued processes
• Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: The white noise case
• On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients
• An \(\infty\)-dimensional inhomogeneous Langevin's equation
• Stochastic partial differential equations for some measure-valued diffusions
• One dimensional stochastic partial differential equations and the branching measure diffusion
• Backward doubly stochastic differential equations and systems of quasilinear SPDEs
• Particle representations for a class of nonlinear SPDEs
• Large deviation for the Fleming-Viot process with neutral mutation and selection
• Mutually catalytic branching in the plane: Infinite measure states
• Large deviations and quasi-potential of a Fleming-Viot process
• Large deviations for the Fleming-Viot process with neutral mutation and selection. II.
• A stochastic log-Laplace equation.
• Nonuniqueness for nonnegative solutions of parabolic stochastic partial differential equations
• Strong uniqueness for an SPDE via backward doubly stochastic differential equations
• The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities
• A limit theorem of branching processes and continuous state branching processes
• On the uniqueness of solutions of stochastic differential equations
• SMALL TIME ASYMPTOTICS FOR FLEMING–VIOT PROCESSES