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Asymptotic expansions for Laplace transforms of Markov processes
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
2018 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 457, no 1, 694-721 p.Article in journal (Refereed) Published
Abstract [en]

Let mu(epsilon) be the probability measures on D[0,T] of suitable Markov processes {xi(epsilon)(t)}0 amp;lt;= t amp;lt;= T (possibly with small jumps) depending on a small parameter epsilon amp;gt;0, where D[0,T] denotes the space of all functions on [0, T] which are right continuous with left limits. In this paper we investigate asymptotic expansions for the Laplace transforms integral(D[0,T]) exp{epsilon F-1(x)}mu(epsilon)(dx) as epsilon -amp;gt; 0 for smooth functionals F on D[0,T]. This study not only recovers several well-known results, but more importantly provides new expansions for jump Markov processes. Besides several standard tools such as exponential change of measures and Taylors expansions, the novelty of the proof is to implement the expectation asymptotic expansions on normal deviations which were recently derived in [13]. (c) 2017 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2018. Vol. 457, no 1, 694-721 p.
Keyword [en]
Laplace transform; Markov process; Cramers transformation; Large deviation; Normal deviation
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-142133DOI: 10.1016/j.jmaa.2017.08.041ISI: 000412152100037OAI: oai:DiVA.org:liu-142133DiVA: diva2:1151725
Available from: 2017-10-24 Created: 2017-10-24 Last updated: 2017-10-24

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Yang, Xiangfeng
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