Hilbert-Space-Valued Super-Brownian Motion and Related Evolution Equations

Journal Article · Sat Jan 15 00:00:00 EST 2000 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S002459911008· OSTI ID:21064278

Kallianpur, G. ^[1]; Sundar, P. ^[2]

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1. Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260 (United States), E-mail: [e-mail]
2. Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803 (United States), E-mail: [e-mail]

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.

• OSTI ID: 21064278
• Journal Information: Applied Mathematics and Optimization, Vol. 41, Issue 1; Other Information: DOI: 10.1007/s002459911008; Copyright (c) 2000 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 2000 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BROWNIAN MOVEMENT
HILBERT SPACE
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL EVOLUTION
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
STOCHASTIC PROCESSES