| Full text | |
| Author(s): |
Olivera, Christian
;
Tudor, Ciprian A.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Annali di Matematica Pura ed Applicata; v. N/A, p. 29-pg., 2025-05-31. |
| Abstract | |
We consider the stochastic heat equation which includes a fractional power of the Laplacian of order alpha is an element of(1,2]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (1, 2]$$\end{document} and it is driven by a nonlinear space-time Gaussian white noise. We study two types of power variations for the solution to this equation: the renormalized quadratic variation and the power variation of order 2 alpha alpha-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{2\alpha }{\alpha -1}$$\end{document}, both over an equidistant partition of the unit interval. We prove that these two sequences admit nontrivial limits when the mesh of the partition goes to zero. We apply these results to identify certain parameters of the stochastic heat equation. (AU) | |
| FAPESP's process: | 20/04426-6 - Stochastic dynamics: analytical and geometrical aspects with applications |
| Grantee: | Paulo Regis Caron Ruffino |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 22/03379-0 - Stochastic and deterministic analysis for irregular models |
| Grantee: | Christian Horacio Olivera |
| Support Opportunities: | Regular Research Grants |