On some first-crossing-time probabilities for a two-dimensional random walk with correlated components

1992 ◽  
Vol 24 (02) ◽  
pp. 441-454
Author(s):  
A. Di Crescenzo ◽  
V. Giorno ◽  
A. G. Nobile
Keyword(s):  
Random Walk ◽  
Algebraic Equation ◽  
Two Dimensional ◽  
Fourth Degree ◽  
Unit Slope ◽  
Crossing Time ◽  
The Mean ◽  
First Crossing Time ◽  
Straight Lines ◽  
Correlated Components

For a two-dimensional random walk {X (n) = (X(n) 1, X(n) 2 )T, n ∈ ℕ0} with correlated components the first-crossing-time probability problem through unit-slope straight lines x 2 = x 1 - r(r = 0,1) is analysed. The p.g.f.'s for the first-crossing-time probabilities are expressed as solutions of a fourth-degree algebraic equation and are then exploited to obtain the first-crossing-time probabilities. Several additional results, including the mean first-crossing time and the probability of ultimate crossing, are also given.

On some first-crossing-time probabilities for a two-dimensional random walk with correlated components

1992 ◽  
Vol 24 (2) ◽  
pp. 441-454 ◽  
Author(s):  
A. Di Crescenzo ◽  
V. Giorno ◽  
A. G. Nobile
Keyword(s):  
Random Walk ◽  
Algebraic Equation ◽  
Two Dimensional ◽  
Fourth Degree ◽  
Unit Slope ◽  
Crossing Time ◽  
The Mean ◽  
First Crossing Time ◽  
Straight Lines ◽  
Correlated Components

For a two-dimensional random walk {X (n) = (X(n)1, X(n)2)T, n ∈ ℕ0} with correlated components the first-crossing-time probability problem through unit-slope straight lines x2 = x1 - r(r = 0,1) is analysed. The p.g.f.'s for the first-crossing-time probabilities are expressed as solutions of a fourth-degree algebraic equation and are then exploited to obtain the first-crossing-time probabilities. Several additional results, including the mean first-crossing time and the probability of ultimate crossing, are also given.

Magnetic Breakdown in a dislocated lattice

1965 ◽  
Vol 287 (1409) ◽  
pp. 165-182 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Random Walk ◽  
Dislocation Density ◽  
Network Model ◽  
Random Phase ◽  
Two Dimensional ◽  
Magnetic Breakdown ◽  
Low Dislocation Density ◽  
Electron Orbit ◽  
Straight Lines

The network model of electron orbits coupled by magnetic breakdown is extended to a two dimensional metal containing dislocations. It is shown that the network is still likely to be a valid representation, but the phase lengths of the arms are altered, and a very low dislocation density (about one per electron orbit) is enough to produce almost complete randomization. The Bloch-like quasi-particles that can travel in straight lines on a perfect network are now heavily scattered, and it is preferable to think of electrons performing a random walk on the arms of the network, although the justification for this procedure is somewhat doubtful. A simpler alternative to Falicov & Sievert’s method is presented for calculating the electrical conductivity of a random-phase network, and is extended to cases where randomness affects only some of the phases, as is believed to be the situation in real metals like zinc and magnesium.

On a symmetry-based constructive approach to probability densities for two-dimensional diffusion processes

1995 ◽  
Vol 32 (2) ◽  
pp. 316-336 ◽  
Author(s):  
A. G. Di Crescenzo ◽  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Diffusion Processes ◽  
Linear Process ◽  
Two Dimensional ◽  
Constructive Approach ◽  
One Dimensional ◽  
Absorbing Boundaries ◽  
Dimensional Diffusion ◽  
Crossing Time ◽  
Probability Densities ◽  
First Crossing Time

The method earlier introduced for one-dimensional diffusion processes [6] is extended to obtain closed form expressions for the transition p.d.f.'s of two-dimensional diffusion processes in the presence of absorbing boundaries and for the first-crossing time p.d.f.'s through such boundaries. Use of such a method is finally made to analyse a two-dimensional linear process.

Searching for a one-dimensional random walker

1974 ◽  
Vol 11 (01) ◽  
pp. 86-93 ◽  
Author(s):  
Bernard J. McCabe
Keyword(s):  
Random Walk ◽  
Wiener Process ◽  
One Dimensional ◽  
Random Walker ◽  
Search Plan ◽  
Crossing Time ◽  
Definition Of ◽  
First Crossing Time ◽  
Finite Moments ◽  
Bernoulli Random Walk

Let {xk } k ≧ − r be a simple Bernoulli random walk with x –r = 0. An integer valued threshold ϕ = {ϕ k } k≧1 is called a search plan if |ϕ k+1−ϕ k |≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ 1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

Searching for a one-dimensional random walker

1974 ◽  
Vol 11 (1) ◽  
pp. 86-93 ◽  
Author(s):  
Bernard J. McCabe
Keyword(s):  
Random Walk ◽  
Wiener Process ◽  
One Dimensional ◽  
Random Walker ◽  
Search Plan ◽  
Crossing Time ◽  
Definition Of ◽  
First Crossing Time ◽  
Finite Moments ◽  
Bernoulli Random Walk

Let {xk}k ≧ − r be a simple Bernoulli random walk with x–r = 0. An integer valued threshold ϕ = {ϕk}k≧1 is called a search plan if |ϕk+1−ϕk|≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

On a symmetry-based constructive approach to probability densities for two-dimensional diffusion processes

1995 ◽  
Vol 32 (02) ◽  
pp. 316-336 ◽  
Author(s):  
A. G. Di Crescenzo ◽  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Diffusion Processes ◽  
Linear Process ◽  
Two Dimensional ◽  
Constructive Approach ◽  
One Dimensional ◽  
Absorbing Boundaries ◽  
Dimensional Diffusion ◽  
Crossing Time ◽  
Probability Densities ◽  
First Crossing Time

The method earlier introduced for one-dimensional diffusion processes [6] is extended to obtain closed form expressions for the transition p.d.f.'s of two-dimensional diffusion processes in the presence of absorbing boundaries and for the first-crossing time p.d.f.'s through such boundaries. Use of such a method is finally made to analyse a two-dimensional linear process.

Distribution of the Lower Boundary Functional of the Step Process of Semi-Markov Random Walk with Delaying Barrier

2018 ◽  
pp. 491-495
Keyword(s):  
Random Walk ◽  
Laplace Transformation ◽  
Lower Boundary ◽  
Step Process ◽  
Zero Level ◽  
Markov Random ◽  
Markov Random Walk ◽  
Crossing Time ◽  
First Crossing Time

In this paper, a step process of semi-Markovian random walk with delaying barrier on the zero-level is constructed and the Laplace transformation of the distribution of first crossing time of this process into the delaying barrier is obtained. Also, the expectation and standard diversion of a boundary functional of the process are given.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

EVALUATION OF LONGO’S HEMORRHOIDECTOMY AT HUE UNIVERSITY HOSPITAL

2012 ◽  
pp. 79-85
Author(s):  
Van Lieu Nguyen ◽  
Doan Van Phu Nguyen ◽  
Thanh Phuc Nguyen
Keyword(s):  
Hospital Stay ◽  
Perioperative Complications ◽  
University Hospital ◽  
Anal Pain ◽  
Stapled Hemorrhoidectomy ◽  
Fourth Degree ◽  
Duration Of Hospital Stay ◽  
The Mean ◽  
Good For

Introduction: Since Longo First described it in 1998, Stapled Hemorrhoidectomy has been emerging as the procedure of choice for symtomatic hemorrhoid. Several studies have shown it to be a safe, effective and relative complication free procedure. The aim of this study was to determine the suitability of (SH) as a day cas procedure at Hue University Hospital. Methods: From Decembre 2009 to April 2012, 384 patients with third- degree and fourth-degree hemorrhoids who underwent Stapled Hemorrhoidectomy were included in this study. Parameters recorded included postoperative complications, analegic requirements, duration of hospital stay and patient satisfaction. Follow-up was performed at 1 month and 3 months post-operative. Results: Of the 384 patients that underwent a Stapled Hemorrhoidectomy 252 (65,7%) were male and 132 (34,3%) were female. The mean age was 47,5 years (range 17-76 years. Duration of hospital stay: The mean day was 2,82 ± 1,15 days (range 1-6 days). There were no perioperative complications. There was one case postoperative complication: hemorrhage; Follow-up after surgery: 286 (74,4%) patients had less anal pain, 78 (20,3%) patients had moderate anal pain, 3 (0,8%) patients had urinary retention; Follow-up after one month: good for 325 (84,6%) patients, average for 59 (15,4%) patients; Follow-up after three months: good for 362 (94,3%) patients, average for 22 (5,7%) patients. Conclusion: Our present study shows that Stapled Hemorrhoidectomy is a safe, reduced postoperative pain, shorter hospital stay and a faster return to unrestricted daily activity

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