Limit theorems for first-passage times in non–linear markov renewal theory

1993 ◽  
Vol 12 (3-4) ◽  
pp. 235-245 ◽  
Author(s):  
Yeongtzay Su
Keyword(s):  
Limit Theorems ◽  
Renewal Theory ◽  
First Passage Times ◽  
First Passage ◽  
Non Linear ◽  
Markov Renewal Theory ◽  
Passage Times

Limit theorems for first-passage times in linear and non-linear renewal theory

1984 ◽  
Vol 16 (04) ◽  
pp. 766-803 ◽  
Author(s):  
S. P. Lalley
Keyword(s):  
Limit Theorems ◽  
Large Deviation ◽  
Local Limit Theorem ◽  
Renewal Theory ◽  
Local Limit ◽  
Linear Boundary ◽  
First Passage ◽  
Non Linear ◽  
First Time ◽  
Passage Times

A local limit theorem for is obtained, where τ a is the first time a random walk Sn with positive drift exceeds a. Applications to large-deviation probabilities and to the crossing of a non-linear boundary are given.

Limit theorems for first-passage times in linear and non-linear renewal theory

1984 ◽  
Vol 16 (4) ◽  
pp. 766-803 ◽  
Author(s):  
S. P. Lalley
Keyword(s):  
Limit Theorems ◽  
Large Deviation ◽  
Local Limit Theorem ◽  
Renewal Theory ◽  
Local Limit ◽  
Linear Boundary ◽  
First Passage ◽  
Non Linear ◽  
First Time ◽  
Passage Times

A local limit theorem for is obtained, where τ a is the first time a random walk Sn with positive drift exceeds a. Applications to large-deviation probabilities and to the crossing of a non-linear boundary are given.

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.

scholarly journals Moment convergence of first-passage times in renewal theory

2016 ◽  
Vol 119 ◽  
pp. 134-143 ◽  
Author(s):  
Alexander Iksanov ◽  
Alexander Marynych ◽  
Matthias Meiners
Keyword(s):  
Renewal Theory ◽  
First Passage Times ◽  
First Passage ◽  
Moment Convergence ◽  
Passage Times
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