Limiting distribution of elliptic homogenization error with periodic diffusion and random potential

AbstractWe find the limiting distribution of , where {Bu}u≧0 is the standard Brownian motion on ℝd, V is a particular random potential and {an}n≧1 is a normalizing sequence.

Download Full-text

A Note on the Accuracy of Normal Approximation of Random Quantities

Calcutta Statistical Association Bulletin ◽

10.1177/00080683211013510 ◽

2021 ◽

Vol 73 (1) ◽

pp. 62-67

Author(s):

Ibrahim A. Ahmad ◽

A. R. Mugdadi

Keyword(s):

Sample Size ◽

Order Statistic ◽

Normal Approximation ◽

Order Approximation ◽

Random Variables ◽

Random Variable ◽

Limiting Distribution ◽

Exact Order ◽

Fixed Sample ◽

Independent Identically Distributed

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

Download Full-text

The geometricity of the limiting distributions in queues and dams

Journal of Applied Probability ◽

10.1017/s0021900200117449 ◽

1993 ◽

Vol 30 (02) ◽

pp. 438-445

Author(s):

R. M. Phatarfod

Keyword(s):

Random Walks ◽

Limiting Distribution ◽

Duality Relation ◽

Limiting Distributions ◽

Initial Term

There are a number of cases in the theories of queues and dams where the limiting distribution of the pertinent processes is geometric with a modified initial term — herein called zero-modified geometric (ZMG). The paper gives a unified treatment of the various cases considered hitherto and some others by using a duality relation between random walks with impenetrable and with absorbing barriers, and deriving the probabilities of absorption by using Waldian identities. Thus the method enables us to distinguish between those cases where the limiting distribution would be ZMG and those where it would not.

Download Full-text

QuickSort: Improved right-tail asymptotics for the limiting distribution, and large deviations (Extended Abstract)

2019 Proceedings of the Sixteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO) ◽

10.1137/1.9781611975505.9 ◽

2019 ◽

pp. 87-93

Author(s):

James Allen Fill ◽

Wei-Chun Hung

Keyword(s):

Large Deviations ◽

Limiting Distribution ◽

Tail Asymptotics

Download Full-text

On random divisions of a convex set

Journal of Applied Probability ◽

10.2307/3213129 ◽

1978 ◽

Vol 15 (3) ◽

pp. 645-649 ◽

Cited By ~ 3

Author(s):

Svante Janson

Keyword(s):

Elementary Proof ◽

Convex Set ◽

Limiting Distribution ◽

Independent Identically Distributed ◽

Normally Distributed

This paper gives an elementary proof that, under some general assumptions, the number of parts a convex set in Rd is divided into by a set of independent identically distributed hyperplanes is asymptotically normally distributed. An example is given where the distribution of hyperplanes is ‘too singular' to satisfy the assumptions, and where a different limiting distribution appears.

Download Full-text

On the continuity of Lyapunov exponents of random walk in random potential

Bernoulli ◽

10.3150/15-bej753 ◽

2017 ◽

Vol 23 (1) ◽

pp. 522-538 ◽

Cited By ~ 1

Author(s):

Le Thi Thu Hien

Keyword(s):

Random Walk ◽

Lyapunov Exponents ◽

Random Potential

Download Full-text

The random division of faces in a planar graph

Advances in Applied Probability ◽

10.2307/1428040 ◽

1996 ◽

Vol 28 (2) ◽

pp. 331-331

Author(s):

Richard Cowan ◽

Simone Chen

Keyword(s):

Planar Graph ◽

Limiting Distribution ◽

Face Type ◽

Connected Planar Graph ◽

Random Division

Consider a connected planar graph. A bounded face is said to be of type k, or is called a k-face, if the boundary of that face contains k edges. Under various natural rules for randomly dividing bounded faces by the addition of new edges, we investigate the limiting distribution of face type as the number of divisions increases.

Download Full-text