Large deviations for Bernstein bridges

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• 作者：Nicolas Privault^a ; ^{nprivault@ntu.edu.sg" class="auth_mail" title="E-mail the corresponding author} ; Xiangfeng Yang^b ; ^{xiangfeng.yang@liu.se" class="auth_mail" title="E-mail the corresponding author} ; Jean-Claude Zambrini^c ; ^{jczambrini@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 60F10 ; 35Q40 ; 60J65
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：126
• 期：5
• 页码：1285-1305
• 全文大小：285 K

文摘

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 pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0304414915002677&_mathId=si1.gif&_user=111111111&_pii=S0304414915002677&_rdoc=1&_issn=03044149&md5=bd91481dc6d0ef2dba65d23d0b65c4bd" title="Click to view the MathML source">ħpan>pan class="mathContainer hidden">pan class="mathCode">$ħ$pan>pan>pan> 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.