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Date of Publication:2022-10-10

Journal:大连理工大学学报

Volume:52

Issue:2

Page Number:309-312

ISSN No.:1000-8608

Abstract:The first exit time of the sum of several Brownian motions in the case
   of Bessel function from an unbounded domain is
   considered.Firstly,general upper and lower asymptotic estimates for the
   first exit time of one Brownian motion from an unbounded open domain
   R~(d+1) are obtained,which are based on a powerful Gaussian technique
   and Slepian′s inequality.Then,the general upper and lower asymptotic
   estimates are considered to the first exit time of the sum of several
   Brownian motions in the case of Bessel function.At first,the first exit
   time probability with moving boundary is considered,then,it′s extended
   to the sum of the number of Brownian motions in the unbounded domain.It
   means that the first exit time of one Brownian motion is suitable for
   the first exit time of the sum of several Brownian motions.

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