Limit theorems for some first passage times

1974 ◽  
Vol 6 (2) ◽  
pp. 241-242
Author(s):  
A. Gut
Keyword(s):  
Limit Theorems ◽  
First Passage Times ◽  
First Passage ◽  
Passage Times

Some asymptotic results for transient random walks

1996 ◽  
Vol 28 (1) ◽  
pp. 207-226 ◽  
Author(s):  
J. Bertoin ◽  
R. A. Doney
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Limit Theorems ◽  
First Passage Times ◽  
Asymptotic Results ◽  
First Passage ◽  
Cramér’S Condition ◽  
Tail Behaviour ◽  
Passage Times ◽  
Asymptotic Tail

We consider a real-valued random walk S which drifts to –∞ and is such that E(exp θS1) < ∞ for some θ > 0, but for which Cramér's condition fails. We investigate the asymptotic tail behaviour of the distributions of the all time maximum, the upwards and downwards first passage times and the last passage times. As an application, we obtain new limit theorems for certain conditional laws.

Some asymptotic results for transient random walks

1996 ◽  
Vol 28 (01) ◽  
pp. 207-226 ◽  
Author(s):  
J. Bertoin ◽  
R. A. Doney
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Limit Theorems ◽  
First Passage Times ◽  
Asymptotic Results ◽  
First Passage ◽  
Cramér’S Condition ◽  
Tail Behaviour ◽  
Passage Times ◽  
Asymptotic Tail

We consider a real-valued random walk S which drifts to –∞ and is such that E(exp θS 1) &lt; ∞ for some θ &gt; 0, but for which Cramér's condition fails. We investigate the asymptotic tail behaviour of the distributions of the all time maximum, the upwards and downwards first passage times and the last passage times. As an application, we obtain new limit theorems for certain conditional laws.

Sign in / Sign up

Export Citation Format

Share Document