scholarly journals The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution

Bernoulli ◽  
2010 ◽  
Vol 16 (4) ◽  
pp. 1016-1038 ◽  
Author(s):  
Thomas Mikosch ◽  
Alfredas Račkauskas
Keyword(s):  
Random Walk ◽  
Size Distribution ◽  
Limit Distribution ◽  
Jump Size ◽  
Distribution Of The Maximum ◽  
Regularly Varying ◽  
Maximum Increment

scholarly journals Persistent random walks may have arbitrarily large tails

1989 ◽  
Vol 21 (1) ◽  
pp. 229-230 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Size Distribution ◽  
Symmetric Random Walk ◽  
Jump Size ◽  
Persistent Random Walks ◽  
Probabilistic Proof

We give a probabilistic proof of a result of Shepp, that a symmetric random walk may have jump size distribution with arbitrarily large tails and yet still be persistent.

scholarly journals Persistent random walks may have arbitrarily large tails

1989 ◽  
Vol 21 (01) ◽  
pp. 229-230
Author(s):  
D. R. Grey
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Size Distribution ◽  
Symmetric Random Walk ◽  
Jump Size ◽  
Persistent Random Walks ◽  
Probabilistic Proof

We give a probabilistic proof of a result of Shepp, that a symmetric random walk may have jump size distribution with arbitrarily large tails and yet still be persistent.

The exponential rate of convergence of the distribution of the maximum of a random walk. Part II

1976 ◽  
Vol 13 (04) ◽  
pp. 733-740
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Real Line ◽  
Exponential Convergence ◽  
Exponential Rate ◽  
The Real ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence ◽  
Successive Maximum

Let Gn (x) be the distribution of the nth successive maximum of a random walk on the real line. Under conditions typical for complete exponential convergence, the decay of Gn (x) – limn→∞ Gn (x) is asymptotically equal to H(x) γn n–3/2 as n → ∞where γ < 1 and H(x) a function solely depending on x. For the case of drift to + ∞, G ∞(x) = 0 and the result is new; for drift to – ∞we give a new proof, simplifying and correcting an earlier version in [9].

The exponential rate of convergence of the distribution of the maximum of a random walk. Part II

1976 ◽  
Vol 13 (4) ◽  
pp. 733-740 ◽  
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Real Line ◽  
Exponential Convergence ◽  
Exponential Rate ◽  
The Real ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence ◽  
Successive Maximum

Let Gn (x) be the distribution of the nth successive maximum of a random walk on the real line. Under conditions typical for complete exponential convergence, the decay of Gn (x) – limn→∞ Gn(x) is asymptotically equal to H(x) γn n–3/2 as n → ∞where γ < 1 and H(x) a function solely depending on x. For the case of drift to + ∞, G∞(x) = 0 and the result is new; for drift to – ∞we give a new proof, simplifying and correcting an earlier version in [9].

Sign in / Sign up

Export Citation Format

Share Document