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Large deviations for Bernstein bridges
School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
Group of Mathematical Physics, University of Lisbon, Lisbon, Portugal.
2016 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 126, no 5, 1285-1305 p.Article in journal (Refereed) Published
Abstract [en]

Bernstein processes over a finite time interval are simultaneously forward and backward Markov processes with arbitrarily fixed initial and terminal probability distributions. In this paper, a large deviation principle is proved for a family of Bernstein processes (depending on a small parameter ħ which is called the Planck constant) arising naturally in Euclidean quantum physics. The method consists in nontrivial Girsanov transformations of integral forms, suitable equivalence forms for large deviations and the (local and global) estimates on the parabolic kernel of the Schrödinger operator.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 126, no 5, 1285-1305 p.
Keyword [en]
Bernstein process; Large deviation principle; Girsanov transformation; Rate function; Schrödinger operator
National Category
Probability Theory and Statistics
URN: urn:nbn:se:liu:diva-126107DOI: 10.1016/ 000373653500001OAI: diva2:911838

Funding agencies:  NTU MOE Tier 2 Grant [ARC3/13]; FCT [PTDC/MAT-STA/0975/2014]

Available from: 2016-03-14 Created: 2016-03-14 Last updated: 2016-05-04

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Yang, Xiangfeng
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Mathematical Statistics Faculty of Science & Engineering
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