Asymptotic behavior of the supremum tail probability for anomalous diffusions

2008 ◽  
Vol 387 (2-3) ◽  
pp. 413-417 ◽  
Author(s):  
Zbigniew Michna
Keyword(s):  
Asymptotic Behavior ◽  
Tail Probability

scholarly journals Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables

2009 ◽  
Vol 2009 ◽  
pp. 1-28 ◽  
Author(s):  
Xin Gao ◽  
Hong Xu ◽  
Dong Ye
Keyword(s):  
Asymptotic Behavior ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Variables ◽  
Tail Probability ◽  
Approximation Methods ◽  
Left And Right

We consider the asymptotic behavior of a probability density function for the sum of any two lognormally distributed random variables that are nontrivially correlated. We show that both the left and right tails can be approximated by some simple functions. Furthermore, the same techniques are applied to determine the tail probability density function for a ratio statistic, and for a sum with more than two lognormally distributed random variables under some stricter conditions. The results yield new insights into the problem of characterization for a sum of lognormally distributed random variables and demonstrate that there is a need to revisit many existing approximation methods.

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.

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