Large and moderate deviations for intersection local times
We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L2...
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| Veröffentlicht in: | Probability theory and related fields 2004-02, Vol.128 (2), p.213-254 |
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| creator | Chen, Xia Li, Wenbo V. |
| description | We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L2-norm of Brownian local times, and coincides with the large deviation obtained by Csorgo, Shi and Yor (1999) for self intersection local times of Brownian bridges. Our approach relies on a Feynman-Kac type large deviation for Brownian occupation time, certain localization techniques from Donsker-Varadhan (1975) and Mansmann (1991), and some general methods developed along the line of probability in Banach space. Our treatment in the case of random walks also involves rescaling, spectral representation and invariance principle. The law of the iterated logarithm for intersection local times is given as an application of our deviation results. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1007/s00440-003-0298-7 |
| format | Article |
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Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L2-norm of Brownian local times, and coincides with the large deviation obtained by Csorgo, Shi and Yor (1999) for self intersection local times of Brownian bridges. Our approach relies on a Feynman-Kac type large deviation for Brownian occupation time, certain localization techniques from Donsker-Varadhan (1975) and Mansmann (1991), and some general methods developed along the line of probability in Banach space. Our treatment in the case of random walks also involves rescaling, spectral representation and invariance principle. The law of the iterated logarithm for intersection local times is given as an application of our deviation results. 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| subjects | Approximation Banach spaces Behavior Brownian motion Deviation Exact sciences and technology Intersections Limit theorems Markov processes Mathematical analysis Mathematics Polymers Probability Probability and statistics Probability theory and stochastic processes Probability theory on algebraic and topological structures Quantum field theory Random walk Random walk theory Rescaling Sciences and techniques of general use Standard deviation Stochastic processes Studies |
| title | Large and moderate deviations for intersection local times |
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