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A Discrete Approach to Rough Parabolic Equations


 
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1. Title Title of document A Discrete Approach to Rough Parabolic Equations
 
2. Creator Author's name, affiliation, country Aurélien Deya; Université de Nancy; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Rough paths theory; Stochastic PDEs; Fractional Brownian motion
 
3. Subject Subject classification 60H05; 60H07; 60G15
 
4. Description Abstract

By combining the formalism of [8] with a discrete approach close to the considerations of [6], we interpret and we solve the rough partial differential equation $$dy_t=Ay_tdt+\sum_{i=1}^mf_i(y_t)dx_t^i, t\in[0,T]$$ on a compact domain $\mathcal{O}$ of $\mathbb{R}^n$, where  $A$ is a rather general elliptic operator of $L^p(\mathcal{O})$, $p>1$, and $f_i(\varphi)(\xi)=f_i(\varphi(\xi))$, and $x$ is the generator of a 2-rough path. The (global) existence, uniqueness and continuity of a solution is established under classical regularity assumptions for $f_i$. Some identification procedures are also provided in order to justify our interpretation of the problem.
 
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7. Date (YYYY-MM-DD) 2011-08-19
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/919
 
10. Identifier Digital Object Identifier 10.1214/EJP.v16-919
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 16
 
12. Language English=en
 
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