## Related Articles

- One-sided local large deviation and renewal theorems in the case of infinite mean. Doney, R. A. // Probability Theory & Related Fields;1997, Vol. 107 Issue 4, p451
Summary. If {S[sub n] ,nâ‰§0} is an integer-valued random walk such that S[sub n] /a[sub n] converges in distribution to a stable law of index Î±âˆˆ (0,1) as nâ†’ âˆž, then Gnedenkoâ€™s local limit theorem provides a useful estimate for P{S[sub n] =r} for values of r such...

- AVAILABILITY ANALYSIS OF PERIODICALLY INSPECTED SYSTEMS WITH RANDOM WALK MODEL. Lirong Cui; Xie, M. // Journal of Applied Probability;Dec2001, Vol. 38 Issue 4, p860
Investigates the instantaneous availability of a system maintained under periodic inspection using random walk models. Importance of system availability to reliability-related decision making; Discussion of two common situations and assumptions; Definition of the random walk model for a...

- Veraverbeke's theorem at large: on the maximum of some processes with negative drift and heavy tail innovations. Barbe, Ph.; McCormick, W. // Extremes;Mar2011, Vol. 14 Issue 1, p63
Veraverbeke's (Stoch Proc Appl 5:27-37, ) theorem relates the tail of the distribution of the supremum of a random walk with negative drift to the tail of the distribution of its increments, or equivalently, the probability that a centered random walk with heavy-tail increments hits a moving...

- Asymptotic Behaviour for Random Walks in Random Environments. Alili, S. // Journal of Applied Probability;Jun99, Vol. 36 Issue 2, p334
Presents information on a study which considered the limit theorems for a random walk in a random environment (RWIRE). Recurrence-transience criteria; Limit theorem for a RWIRE with positive drift; Ergodic environments.

- Rates of convergence of random walk on distance regular graphs. Belsley, Eric David // Probability Theory & Related Fields;1998, Vol. 112 Issue 4, p493
When run on any non-bipartite q-distance regular graph from a family containing graphs of arbitrarily large diameter d, we show that d steps are necessary and sufficient to drive simple random walk to the uniform distribution in total variation distance, and that a sharp cutoff phenomenon...

- An effective criterion for ballistic behavior of random walks in random environment. Sznitman, Alain-Sol // Probability Theory & Related Fields;2002, Vol. 122 Issue 4, p509
We investigate multi-dimensional random walks in random environment. Specifically, we provide an effective criterion which can be checked by inspection of the environment in a finite box, and implies a ballistic strong law of large numbers, a central limit theorem and several large deviation...

- Algorithm to determine the optimal parameters of a polynomial Wiener filter-extrapolator for nonstationary stochastic processes observed with errors. Atamanyuk, I. P. // Cybernetics & Systems Analysis;Mar2011, Vol. 47 Issue 2, p305
The apparatus of canonical expansions of stochastic processes is used to obtain an algorithm to determine the optimal parameters of a discrete polynomial Wiener filter-extrapolator for nonstationary stochastic processes with errors.

- A Note on the Ruin Probability in the Delayed Renewal Risk Model. Chun Su; Qihe Tang // Southeast Asian Bulletin of Mathematics;2005, Vol. 29 Issue 5, p969
Veraverbeke (1977, Stochastic Processes Appl. 5, no. 1, 27-37) and Embrechts and Veraverbeke (1982, Insurance Math. Econom. 1, no. 1, 55-72) obtained that there is a simple asymptotic relation for the ruin probability in the renewal risk model under the assumption that the claim size is heavy...

- Random Walk on the Incipient Infinite Cluster for Oriented Percolation in High Dimensions. Barlow, Martin T.; Járai, Antal A.; Kumagai, Takashi; Slade, Gordon // Communications in Mathematical Physics;Feb2008, Vol. 278 Issue 2, p385
We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on $${\mathbb{Z}}^{d} \times {\mathbb{Z}}_+$$ . In dimensions d > 6, we obtain bounds on exit times, transition probabilities, and the range of the random walk, which establish that...

- Editorial introduction. Miyazawa, Masakiyo; Zhao, Yiqiang // Queueing Systems;Jun2013, Vol. 74 Issue 2/3, p105
An introduction is presented in which the editors discuss various reports within the issue on topics including tail asymptotic behaviors of two-dimensional reflecting random walks, general dimensional reflecting process and large scale system for telecommunications.