Thumbnail

Non-linear rough heat equations

Deya, Aurélien; Gubinelli, Massimiliano; Tindel, Samy (2012), Non-linear rough heat equations, Probability Theory and Related Fields, 153, 1-2, p. 97-147. http://dx.doi.org/10.1007/s00440-011-0341-z

View/Open
Type
Article accepté pour publication ou publié
Date
2012
Journal name
Probability Theory and Related Fields
Volume
153
Number
1-2
Publisher
Springer
Pages
97-147
Publication identifier
Metadata
Show full item record
Author(s)
Deya, Aurélien
Gubinelli, Massimiliano
Tindel, Samy
Abstract (EN)
This article is devoted to define and solve an evolution equation of the form dy t = Δy t dt + dX t (y t ), where Δ stands for the Laplace operator on a space of the form Lp(\mathbb Rn)Lp(Rn), and X is a finite dimensional noisy nonlinearity whose typical form is given by Xt(j)=åi=1N xit fi(j)Xt()=Ni=1xitfi() , where each x = (x (1), … , x (N)) is a γ-Hölder function generating a rough path and each f i is a smooth enough function defined on Lp(\mathbb Rn)Lp(Rn). The generalization of the usual rough path theory allowing to cope with such kind of system is carefully constructed.
Subjects / Keywords
Rough paths theory; Stochastic PDEs; Fractional Brownian motion