# Journal article

## Transition probability of Brownian motion in the octant and its application to default modelling

Abstract:

We derive a semi-analytical formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main theoretical result is a solution to the original problem expressed as an expansion into special functions and an eigenvalue which has to be chosen to allow a matching of the ...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Accepted manuscript, pdf, 1006.4KB)
Publisher copy:
10.1080/1350486X.2018.1481439

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Catherine's College
Role:
Author
ORCID:
0000-0003-4027-5298
Publisher:
Routledge Publisher's website
Journal:
Applied Mathematical Finance Journal website
Volume:
25
Issue:
5-6
Pages:
434-465
Publication date:
2018-06-18
Acceptance date:
2018-05-22
DOI:
EISSN:
1466-4313
ISSN:
1350-486X
Keywords:
Pubs id:
pubs:853485
UUID:
uuid:093c9f6a-ffba-4101-91d3-6fb87fb3687a
Local pid:
pubs:853485
Source identifiers:
853485
Deposit date:
2018-05-22