4 papers · 1 filter
Asymptotic behavior of the stochastic heat equation over large intervals
David Candil, Robert C. Dalang, Marta Sanz Solé
We consider a nonlinear stochastic heat equation on , driven by a space-time white noise , with a given initial condition an…
Sharp upper bounds on hitting probabilities for the solution to the stochastic heat equation on the line
Robert C. Dalang, David Nualart, Fei Pu
For Gaussian random fields with values in , sharp upper and lower bounds on the probability of hitting a fixed set have been available for many years. These apply in…
Stochastic Partial Differential Equations, Space-time White Noise and Random Fields
Robert C. Dalang, Marta Sanz-Solé
This book is an introduction to the theory of stochastic partial differential equations (SPDEs), using the random field approach pioneered by J.B. Walsh (1986). It consists of two…
Sample path properties of parabolic SPDEs with non constant coefficients
Robert C. Dalang, Marta Sanz-Solé
We consider an SPDE driven by a parabolic second order partial differential operator with a nonlinear random external forcing defined by a Gaussian noise that is white in time and…