Local behavior and hitting probabilities of the process

We obtain a formula for the -dimensional distributions of the process in terms of a Fredholm determinant on , as opposed to the standard formula which involves extended kernels, on . The formula is analogous to an earlier formula of Prähofer and Spohn (J Stat Phys 108(5–6):1071–1106, 2002 ) for the...

Full description

Saved in:
Bibliographic Details
Published inProbability theory and related fields Vol. 157; no. 3-4; pp. 605 - 634
Main Authors Quastel, Jeremy, Remenik, Daniel
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2013
Springer Nature B.V
Subjects
Brownian motion
Economics
Finance
Insurance
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Theoretical
60K35
60G17
82C22
Online AccessGet full text

Cover

More Information
Summary:We obtain a formula for the -dimensional distributions of the process in terms of a Fredholm determinant on , as opposed to the standard formula which involves extended kernels, on . The formula is analogous to an earlier formula of Prähofer and Spohn (J Stat Phys 108(5–6):1071–1106, 2002 ) for the process. Using this formula we are able to prove that the process is Hölder continuous with exponent —and that it fluctuates locally like a Brownian motion. We also explain how the same methods can be used to obtain the analogous results for the process. As a consequence of these two results, we derive a formula for the continuum statistics of the process, analogous to that obtained in Corwin et al. (Commun Math Phys 2011 , to appear) for the process.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-012-0466-8