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Asymptotics of exponential moments of a weighted local time of a Brownian motion with small variance
Volume 3, Issue 1 (2016), pp. 95–103
Alexei Kulik   Daryna Sobolieva  

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https://doi.org/10.15559/16-VMSTA49
Pub. online: 5 April 2016      Type: Research Article      Open accessOpen Access

Received
9 December 2015
Revised
22 February 2016
Accepted
29 February 2016
Published
5 April 2016

Abstract

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon \to 0$.

References

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Chiang, T.S., Sheu, S.J.: Small perturbations of diffusions in inhomogeneous media. Ann. Inst. Henri Poincaré 38, 285–318 (2002). MR1899455. doi:10.1016/S0246-0203(01)01101-3
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Dynkin, E.B.: Markov Processes. Springer, Berlin, Göttingen, Heidelberg (1965). MR0193671
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Freidlin, M.I., Wentzell, A.D.: Random Perturbations of Dynamical Systems. Springer, New York (1984). MR0722136. doi:10.1007/978-1-4684-0176-9
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Itô, K., McKean, H.P.: Diffusion Processes and Their Sample Paths. Springer (1965). MR0345224
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Krykun, I.H.: Large deviation principle for stochastic equations with local time. Theory Stoch. Process. 15(31), 140–155 (2009). MR2598533
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Kulik, A.M., Soboleva, D.D.: Large deviations for one-dimensional SDE with discontinuous diffusion coefficient. Theory Stoch. Process. 18(34), 101–110 (2012). MR3124766
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Sobolieva, D.D.: Large deviations for one-dimensional SDEs with discontinuous coefficients. Theory Stoch. Process. 18(34), 102–108 (2012). MR3124779
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Sznitman, A.S.: Brownian Motion, Obstacles and Random Media. Springer, Germany (1998). MR1717054. doi:10.1007/978-3-662-11281-6

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© 2016 The Author(s). Published by VTeX
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Keywords
Local time exponential moment large deviations principle

MSC2010
60J55 60F10 60H10

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