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On Convergence of Population Processes in Random Environments to the Stochastic Heat Equation with Colored Noise
- Source :
- Electron. J. Probab.
- Publication Year :
- 2003
- Publisher :
- The Institute of Mathematical Statistics and the Bernoulli Society, 2003.
-
Abstract
- We consider the stochastic heat equation with a multiplicative colored noise term on the real space for dimensions greater or equal to 1. First, we prove convergence of a branching particle system in a random environment to this stochastic heat equation with linear noise coefficients. For this stochastic partial differential equation with more general non-Lipschitz noise coefficients we show convergence of associated lattice systems, which are infinite dimensional stochastic differential equations with correlated noise terms, provided that uniqueness of the limit is known. In the course of the proof, we establish existence and uniqueness of solutions to the lattice systems, as well as a new existence result for solutions to the stochastic heat equation. The latter are shown to be jointly continuous in time and space under some mild additional assumptions.
- Subjects :
- Statistics and Probability
Stochastic control
Continuous-time stochastic process
60J80
Partial differential equation
Differential equation
superprocess
random environment
Heat equation
Mathematical analysis
First-order partial differential equation
stochastic partial differential equation
Stochastic partial differential equation
Stochastic differential equation
60K37
Quantum stochastic calculus
colored noise
60K35
60F05
60H15
particle representation
weak convergence
Statistics, Probability and Uncertainty
existence theorem
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Electron. J. Probab.
- Accession number :
- edsair.doi.dedup.....e67d1f269a987f0125c0a2aadf02078a