Well-posedness of the martingale problem for super-Brownian motion with interactive branching
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Abstract
In this paper a martingale problem for super-Brownian motion with interactive branching is derived. The uniqueness of the solution to the martingale problem is obtained by using the pathwise uniqueness of the solution to a corresponding system of SPDEs with proper boundary conditions. The existence of the solution to the martingale problem and the local Hölder continuity of the density process are also studied.Keywords
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This publication has 21 references indexed in Scilit:
- Existence and pathwise uniqueness to an SPDE driven by -stable colored noiseStochastic Processes and their Applications, 2019
- Superprocesses with interaction and immigrationStochastic Processes and their Applications, 2016
- Stochastic equations of super-Lévy processes with general branching mechanismStochastic Processes and their Applications, 2014
- Partial Differential Equations2010
- Conditional Log-Laplace Functionals of Immigration Superprocesses with Dependent Spatial MotionActa Applicandae Mathematicae, 2005
- Construction of immigration superprocesses with dependent spatial motion from one-dimensional excursionsProbability Theory and Related Fields, 2003
- On the martingale problem for interactive measure-valued branching diffusionsMemoirs of the American Mathematical Society, 1995
- Martingale measures and stochastic calculusProbability Theory and Related Fields, 1990
- An ∞-dimensional inhomogeneous Langevin's equationJournal of Functional Analysis, 1985
- On the discrete analogues of some generalizations of Gronwall's inequalityMonatshefte für Mathematik, 1965