Two Contrasting Properties of Solutions for One-Dimensional Stochastic Partial Differential Equations
- 1 April 1994
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 46 (2) , 415-437
- https://doi.org/10.4153/cjm-1994-022-8
Abstract
The paper is concerned with the comparison of two solutions for a one-dimensional stochastic partial differential equation. Noting that support compactness of solutions propagates with passage of time, we define the SCP property and show that the SCP property and the strong positivity are two contrasting properties of solutions for one-dimensional SPDEs, which are due to degeneracy of the noise-term coefficientKeywords
This publication has 9 references indexed in Scilit:
- On the support of solutions to the heat equation with noiseStochastics and Stochastic Reports, 1991
- Derivation of the hydrodynamical equation for one-dimensional Ginzburg-Landau modelProbability Theory and Related Fields, 1989
- One dimensional stochastic partial differential equations and the branching measure diffusionProbability Theory and Related Fields, 1989
- Stochastic partial differential equations for some measure-valued diffusionsProbability Theory and Related Fields, 1988
- On the Supports of Measure-Valued Critical Branching Brownian MotionThe Annals of Probability, 1988
- An infinite dimensional stochastic differential equation with state spaceC(ℝ)Probability Theory and Related Fields, 1987
- Large fluctuations for a nonlinear heat equation with noiseJournal of Physics A: General Physics, 1982
- Wandering Random Measures in the Fleming-Viot ModelThe Annals of Probability, 1982
- Stochastic evolution equations and related measure processesJournal of Multivariate Analysis, 1975