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References (7)
-
E. Dynkin (1994)
An introduction to branching measure-valued processes -
Toshio Yamada, Shinzo Watanabe (1971)
On the uniqueness of solutions of stochastic difierential equations -
D. Dawson (1993)
Measure-valued Markov processes -
I. Karatzas (1987)
Brownian Motion and Stochastic CalculusElearn
-
N. Krylov, B. Rozovskii (1981)
Stochastic evolution equationsJournal of Soviet Mathematics, 16
-
N. Konno, T. Shiga (1988)
Stochastic partial differential equations for some measure-valued diffusionsProbability Theory and Related Fields, 79
-
D. Stroock, Srinivasa Varadhan (1979)
Multidimensional Diffusion Processes
- Publisher
- Springer Journals
- Copyright
- Copyright © Inc. by 2000 Springer-Verlag New York
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s002459911008
- Publisher site
- See Article on Publisher Site
Abstract
A stochastic partial differential equation in which the square root of the solution appears as the diffusion coefficient is studied as a particular case of stochastic evolution equations. Weak existence of a solution is proved by the Euler approximation scheme. The super-Brownian motion on [0, 1] is also studied as a Hilbert-space-valued equation. In this set up, weak existence, pathwise uniqueness, and positivity of solutions are obtained in any dimension d .
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2008