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.

Some asymptotic results for transient random walks with applications to insurance risk

2001 ◽  
Vol 38 (01) ◽  
pp. 108-121 ◽  
Author(s):  
Aleksandras Baltrūnas
Keyword(s):  
Random Walk ◽  
Ruin Probability ◽  
Risk Theory ◽  
Insurance Risk ◽  
Asymptotic Results ◽  
First Passage ◽  
Tail Behaviour ◽  
Heavy Tailed ◽  
Exact Rate Of Convergence ◽  
Passage Times

We consider a real-valued random walk which drifts to -∞ and is such that the step distribution is heavy tailed, say, subexponential. We investigate the asymptotic tail behaviour of the distribution of the upwards first passage times. As an application, we obtain the exact rate of convergence for the ruin probability in finite time. Our result supplements similar theorems in risk theory.

Some asymptotic results for transient random walks with applications to insurance risk

2001 ◽  
Vol 38 (1) ◽  
pp. 108-121 ◽  
Author(s):  
Aleksandras Baltrūnas
Keyword(s):  
Random Walk ◽  
Ruin Probability ◽  
Risk Theory ◽  
Insurance Risk ◽  
Asymptotic Results ◽  
First Passage ◽  
Tail Behaviour ◽  
Heavy Tailed ◽  
Exact Rate Of Convergence ◽  
Passage Times

We consider a real-valued random walk which drifts to -∞ and is such that the step distribution is heavy tailed, say, subexponential. We investigate the asymptotic tail behaviour of the distribution of the upwards first passage times. As an application, we obtain the exact rate of convergence for the ruin probability in finite time. Our result supplements similar theorems in risk theory.

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