Gerhold, S. (2023). Small ball probabilities and large deviations for grey Brownian motion. Electronic Communications in Probability, 28, 1–8. https://doi.org/10.1214/23-ECP555
E105-01 - Forschungsbereich Risikomanagement in Finanz- und Versicherungsmathematik
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Journal:
Electronic Communications in Probability
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ISSN:
1083-589X
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Date (published):
2023
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Number of Pages:
8
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Publisher:
Institute of Mathematical Statistics (IMS)
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Peer reviewed:
Yes
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Keywords:
fractional Brownian motion; grey Brownian motion; large deviations; small ball probabilities; small deviations; Wright M-function
en
Abstract:
We show that the uniform norm of generalized grey Brownian motion over the unit interval has an analytic density, excluding the special case of fractional Brownian motion. Our main result is an asymptotic expansion for the small ball probability of generalized grey Brownian motion, which extends to other norms on path space. The decay rate is not exponential but polynomial, of degree two. For the uniform norm and the Hölder norm, we also prove a large deviations estimate.
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