# Journal article

## Smooth random functions, random ODEs, and Gaussian processes

Abstract:

The usual way in which mathematicians work with randomness is by a rigorous formulation of the idea of Brownian motion, which is the limit of a random walk as the step length goes to zero. A Brownian path is continuous but nowhere differentiable, and this nonsmoothness is associated with technical complications that can be daunting. However, there is another approach to random processes that is more elementary, involving smooth random functions defined by finite Fourier series with random coe...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Version of record, pdf, 2.4MB)
Publisher copy:
10.1137/17M1161853

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Society for Industrial and Applied Mathematics Publisher's website
Journal:
SIAM Review Journal website
Volume:
61
Issue:
1
Pages:
185–205
Publication date:
2019-02-07
Acceptance date:
2018-05-31
DOI:
EISSN:
1095-7200
ISSN:
0036-1445
Keywords:
Pubs id:
pubs:854686
UUID:
Local pid:
pubs:854686
Source identifiers:
854686
Deposit date:
2018-06-02