# The Prepared Practitioner

## Related Articles

- Simple transient random walks in one-dimensional random environment: the central limit theorem. Goldsheid, Ilya Ya. // Probability Theory & Related Fields;Sep2007, Vol. 139 Issue 1/2, p41
We consider a simple random walk (dimension one, nearest neighbour jumps) in a quenched random environment. The goal of this work is to provide sufficient conditions, stated in terms of properties of the environment, under which the central limit theorem (CLT) holds for the position of the walk....

- The central limit theorem for the Smoluchovski coagulation model. Kolokoltsov, Vassili N. // Probability Theory & Related Fields;Jan2010, Vol. 146 Issue 1/2, p87
The general model of coagulation is considered. For basic classes of unbounded coagulation kernels the central limit theorem (CLT) is obtained for the fluctuations around the dynamic law of large numbers (LLN) described by the Smoluchovski equation. A rather precise rate of convergence is given...

- On the Central Limit Theorems for Forward and Backward Martingales. Yilun Shang // World Academy of Science, Engineering & Technology;Apr2011, Issue 52, p860
Let {Xi}iâ‰¥1 be a martingale difference sequence with Xi = Si - Si-1. Under some regularity conditions, we show that Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed.-1/2SNn is asymptotically normal, where {Ni}iâ‰¥1 is a sequence of positive...

- Almost sure central limit theorem without logarithmic sums. Martikainen, A. // Journal of Mathematical Sciences;Aug2006, Vol. 137 Issue 1, p4549
We investigate possible rates of convergence in the almost sure central limit theorem for sums of independent random variables and martingales. Bibliography: 9 titles.

- NECKLACE PROCESSES VIA PÃ“LYA URNS. Nakata, Toshio // Journal of Applied Probability;Mar2009, Vol. 46 Issue 1, p284
Mallows and Shepp (2008) developed the following necklace processes. Start with a necklace consisting of one white bead and one black bead, and insert, one at a time, under a deterministic rule, a white bead or a black bead between a randomly chosen adjacent pair. They studied the statistical...

- A UNIFYING PROBABILITY EXAMPLE. Maruszewski, Jr., Richard F. // Mathematics & Computer Education;Fall2002, Vol. 36 Issue 3, p213
The article presents a study related to probability and mathematical statistics. The purpose of this study is to discuss an example from probability and statistics which ties together several various topics. The topics include the mean and variance of a discrete random variable, the mean and...

- Fisher information inequalities and the central limit theorem. Johnson, Oliver; Barron, Andrew // Probability Theory & Related Fields;Jul2004, Vol. 129 Issue 3, p391
We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincarï¿½ inequalities, to provide a better understanding of the decrease in Fisher information implied by results...

- On the central limit theorem for geometrically ergodic Markov chains. H�ggstr�m, Olle // Probability Theory & Related Fields;May2005, Vol. 132 Issue 1, p74
LetX0,X1,... be a geometrically ergodic Markov chain with state spaceand stationary distributionp. It is known that ifh:?Rsatisfiesp(|h|2+?)<8 for some ?>0, then the normalized sums of theX iï¿½s obey a central limit theorem. Here we show, by means of a counterexample, that the...

- Foundations of Quantum Mechanics: The Connection Between QM and the Central Limit Theorem. Olavo, L. S. F. // Foundations of Physics;Jun2004, Vol. 34 Issue 6, p891
In this paper we unravel the connection between the quantum mechanical formalism and the Central limit theorem (CLT). We proceed to connect the results coming from this theorem with the derivations of the SchrÃ¶dinger equation from the Liouville equation, presented by ourselves in other...