The first-passage time sSðxÞ of a one-dimensional continuous stochastic process XðtÞ, starting from x Sð0Þ, through a smooth boundary S(t) is investigated; in particular, diffusions and some kinds of Gaussian processes, such as Gauss-Markov and their fractional integrals, are considered. The tail behavior of Pðmaxs2½0, tXðsÞ > RÞ and related asymptotics for sSðxÞ are obtained, and some examples are reported.
Abundo, M. (2021). On the first-passage times of certain Gaussian processes, and related asymptotics. STOCHASTIC ANALYSIS AND APPLICATIONS, 39(4), 712-727 [10.1080/07362994.2020.1843495].
On the first-passage times of certain Gaussian processes, and related asymptotics
Abundo, Mario
2021-01-01
Abstract
The first-passage time sSðxÞ of a one-dimensional continuous stochastic process XðtÞ, starting from x Sð0Þ, through a smooth boundary S(t) is investigated; in particular, diffusions and some kinds of Gaussian processes, such as Gauss-Markov and their fractional integrals, are considered. The tail behavior of Pðmaxs2½0, tXðsÞ > RÞ and related asymptotics for sSðxÞ are obtained, and some examples are reported.File in questo prodotto:
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