<div class="csl-bib-body">
<div class="csl-entry">Gerhold, S. (2023). Small ball probabilities and large deviations for grey Brownian motion. <i>Electronic Communications in Probability</i>, <i>28</i>, 1–8. https://doi.org/10.1214/23-ECP555</div>
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dc.identifier.issn
1083-589X
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/192375
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dc.description.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.
en
dc.language.iso
en
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dc.publisher
Institute of Mathematical Statistics (IMS)
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dc.relation.ispartof
Electronic Communications in Probability
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
fractional Brownian motion
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dc.subject
grey Brownian motion
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dc.subject
large deviations
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dc.subject
small ball probabilities
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dc.subject
small deviations
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dc.subject
Wright M-function
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dc.title
Small ball probabilities and large deviations for grey Brownian motion
