Precise Asymptotic Formulae for the First Hitting Times of Bessel Processes

2018 ◽  
Vol 41 (2) ◽  
pp. 603-615
Author(s):  
Yuji HAMANA ◽  
Hiroyuki MATSUMOTO
Keyword(s):  
Hitting Times ◽  
Bessel Processes ◽  
Asymptotic Formulae ◽  
First Hitting Times ◽  
Precise Asymptotic

scholarly journals Asymptotic expansions for the first hitting times of Bessel processes

2021 ◽  
Vol 41 (4) ◽  
pp. 509-537
Author(s):  
Yuji Hamana ◽  
Ryo Kaikura ◽  
Kosuke Shinozaki
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Expansions ◽  
Tail Probability ◽  
Bessel Process ◽  
Hitting Times ◽  
First Hitting Time ◽  
Bessel Processes ◽  
The Third ◽  
First Hitting Times ◽  
Precise Asymptotic

We study a precise asymptotic behavior of the tail probability of the first hitting time of the Bessel process. We deduce the order of the third term and decide the explicit form of its coefficient.

scholarly journals First Hitting Times to Intermittent Targets

2019 ◽  
Vol 123 (25) ◽  
Author(s):  
Gabriel Mercado-Vásquez ◽  
Denis Boyer
Keyword(s):  
Hitting Times ◽  
First Hitting Times

Examples for the Theory of Strong Stationary Duality with Countable State Spaces

1990 ◽  
Vol 4 (2) ◽  
pp. 157-180 ◽  
Author(s):  
Persi Diaconis ◽  
James Allen Fill
Keyword(s):  
Stopping Time ◽  
Renewal Theory ◽  
Hitting Times ◽  
State Spaces ◽  
Ergodic Markov Chain ◽  
Countable State Space ◽  
Strong Stationary Duality ◽  
Countable State ◽  
Infinite State ◽  
First Hitting Times

Let X1,X2,… be an ergodic Markov chain on the countable state space. We construct a strong stationary dual chain X* whose first hitting times give sharp bounds on the convergence to stationarity for X. Examples include birth and death chains, queueing models, and the excess life process of renewal theory. This paper gives the first extension of the stopping time arguments of Aldous and Diaconis [1,2] to infinite state spaces.

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