Hilbert-space-valued super-Brownian motion and related evolution equations
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.
Publication Source (Journal or Book title)
Applied Mathematics and Optimization
Kallianpur, G., & Sundar, P. (2000). Hilbert-space-valued super-Brownian motion and related evolution equations. Applied Mathematics and Optimization, 41 (1), 141-154. https://doi.org/10.1007/s002459911008