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This article is cited in 20 scientific papers (total in 20 papers)
Martingales and first passage times for Ornstein–Uhlenbeck processes with a jump component
A. A. Novikov
University of Technology, Sydney
Abstract:
Using martingale technique, we show that a distribution of the first-passage time over a level for the Ornstein–Uhlenbeck process with jumps is exponentially bounded. In the case of absence of positive jumps, the Laplace transform for this passage time is found. Further, the maximal inequalities are also given when the marginal distribution is stable.
Keywords:
exponential martingales, first-passage times, Ornstein–Uhlenbeck process, Laplace transform, moment Wald's identity, maximal inequalities, stable distribution.
DOI:
https://doi.org/10.4213/tvp288
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English version:
Theory of Probability and its Applications, 2004, 48:2, 288–303
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Received: 23.01.2003
Citation:
A. A. Novikov, “Martingales and first passage times for Ornstein–Uhlenbeck processes with a jump component”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 340–358; Theory Probab. Appl., 48:2 (2004), 288–303
Citation in format AMSBIB
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\jour Theory Probab. Appl.
\yr 2004
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\pages 288--303
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http://mi.mathnet.ru/eng/tvp288https://doi.org/10.4213/tvp288 http://mi.mathnet.ru/eng/tvp/v48/i2/p340
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Jacobsen M., Jensen A.T., “Exit times for a class of piecewise exponential Markov processes with two–sided jumps”, Stochastic Process. Appl., 117:9 (2007), 1330–1356
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A. A. Novikov, “On Distributions of First Passage Times and Optimal Stopping of AR(1) Sequences”, Theory Probab. Appl., 53:3 (2009), 419–429
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