scholarly journals A symmetric Random Walk defined by the time-one map of a geodesic flow

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Pablo D. Carrasco ◽  
◽  
Túlio Vales
Keyword(s):  
Random Walk ◽  
Geodesic Flow ◽  
Symmetric Random Walk

A Berry-Esseen Type Theorem on Nilpotent Covering Graphs

2004 ◽  
Vol 56 (5) ◽  
pp. 963-982 ◽  
Author(s):  
Satoshi Ishiwata
Keyword(s):  
Random Walk ◽  
Transition Probability ◽  
Type Theorem ◽  
Speed Of Convergence ◽  
Complete Proof ◽  
Symmetric Random Walk ◽  
Markov Kernel ◽  
Covering Graph

AbstractWe prove an estimate for the speed of convergence of the transition probability for a symmetric random walk on a nilpotent covering graph. To obtain this estimate, we give a complete proof of the Gaussian bound for the gradient of the Markov kernel.

Some Results in a Correlated Random Walk

1971 ◽  
Vol 14 (3) ◽  
pp. 341-347 ◽  
Author(s):  
G. C. Jain
Keyword(s):  
Random Walk ◽  
Joint Distribution ◽  
Statistical Problem ◽  
Correlated Random Walk ◽  
Symmetric Random Walk

In connection with a statistical problem concerning the Galtontest Cśaki and Vincze [1] gave for an equivalent Bernoullian symmetric random walk the joint distribution of g and k, denoting respectively the number of positive steps and the number of times the particle crosses the origin, given that it returns there on the last step.

scholarly journals Two explicit Skorokhod embeddings for simple symmetric random walk

2019 ◽  
Vol 129 (9) ◽  
pp. 3431-3445 ◽  
Author(s):  
Xue Dong He ◽  
Sang Hu ◽  
Jan Obłój ◽  
Xun Yu Zhou
Keyword(s):  
Random Walk ◽  
Symmetric Random Walk

scholarly journals The Maximum of a Random Walk and Its Application to Rectangle Packing

1998 ◽  
Vol 12 (3) ◽  
pp. 373-386 ◽  
Author(s):  
E. G. Coffman ◽  
Philippe Flajolet ◽  
Leopold Flatto ◽  
Micha Hofri
Keyword(s):  
Random Walk ◽  
Upper Bound ◽  
Symmetric Random Walk ◽  
Rectangle Packing ◽  
Unit Width ◽  
Minimum Height ◽  
Image Position

Let S0,…,Sn be a symmetric random walk that starts at the origin (S0 = 0) and takes steps uniformly distributed on [— 1,+1]. We study the large-n behavior of the expected maximum excursion and prove the estimate,where c = 0.297952.... This estimate applies to the problem of packing n rectangles into a unit-width strip; in particular, it makes much more precise the known upper bound on the expected minimum height, O(n½), when the rectangle sides are 2n independent uniform random draws from [0,1].

Some joint distributions in Bernoulli excursions

1994 ◽  
Vol 31 (A) ◽  
pp. 239-250
Author(s):  
Endre Csáki
Keyword(s):  
Random Walk ◽  
Random Variables ◽  
Characteristic Functions ◽  
Symmetric Random Walk ◽  
Joint Distributions ◽  
Recursion Formulas

Some exact and asymptotic joint distributions are given for certain random variables defined on the excursions of a simple symmetric random walk. We derive appropriate recursion formulas and apply them to get certain expressions for the joint generating or characteristic functions of the random variables.

On the geometric ergodicity of hybrid samplers

2003 ◽  
Vol 40 (1) ◽  
pp. 123-146 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
G. O. Roberts ◽  
J. S. Rosenthal
Keyword(s):  
Random Walk ◽  
Sufficient Conditions ◽  
Metropolis Algorithm ◽  
Geometric Ergodicity ◽  
Target Density ◽  
Symmetric Random Walk ◽  
Uniform Ergodicity ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) on ℝd. This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implying V-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.

On the geometric ergodicity of hybrid samplers

2003 ◽  
Vol 40 (01) ◽  
pp. 123-146 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
G. O. Roberts ◽  
J. S. Rosenthal
Keyword(s):  
Random Walk ◽  
Sufficient Conditions ◽  
Metropolis Algorithm ◽  
Geometric Ergodicity ◽  
Target Density ◽  
Symmetric Random Walk ◽  
Uniform Ergodicity ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) on ℝ d . This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implying V-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.

Joint asymptotic behavior of local and occupation times of random walk in higher dimension

2007 ◽  
Vol 44 (4) ◽  
pp. 535-563 ◽  
Author(s):  
Endre Csáki ◽  
Antónia Földes ◽  
Pál Révész
Keyword(s):  
Asymptotic Behavior ◽  
Random Walk ◽  
Unit Ball ◽  
Local Time ◽  
Occupation Time ◽  
Local Times ◽  
Higher Dimension ◽  
Occupation Times ◽  
Symmetric Random Walk

Considering a simple symmetric random walk in dimension d ≧ 3, we study the almost sure joint asymptotic behavior of two objects: first the local times of a pair of neighboring points, then the local time of a point and the occupation time of the surface of the unit ball around it.

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