TITLE

# Doing analysis by tossing a coin

AUTHOR(S)
Stroock, Daniel W.
PUB. DATE
March 2000
SOURCE
Mathematical Intelligencer;Spring2000, Vol. 22 Issue 2, p66
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Provides an example of the role of probabilistic natural considerations in understanding real analysis. Implications of the given example for the reputation of continuous monotone singular functions; Context of the weak law of large numbers; Representation of coin-tossing game outcomes as real numbers; Concerns on the non-random factor of the measure theory.
ACCESSION #
3142451

## Related Articles

• A Strong Limit Theorem for Weighted Sums of Sequences of Negatively Dependent Random Variables. Qunying Wu // Journal of Inequalities & Applications;2010, Vol. 2010, p1

Applying the moment inequality of negatively dependent random variables which was obtained by Asadian et al. (2006), the strong limit theorem for weighted sums of sequences of negatively dependent random variables is discussed. As a result, the strong limit theorem for negatively dependent...

• Note on w-limit set of a graph map. Taixiang Sun; Hongjian Xi; Hailan Liang // Journal of Computational Analysis & Applications;Nov2011, Vol. 13 Issue 7, p1268

Let G be a graph and f : G ? G be continuous. Denote by R(f)ï¿½ and ?(f) the closure of the set of recurrent points and ca-limit set of f respectively. In this paper, we show that: (1) If x ? ?(f) - R(f)ï¿½, then ?(x, f) is an infinite minimal set. (2) If f is piecewise monotone, then ?(f)...

• FASTEST COUPLING OF RANDOM WALKS. ROGERS, L. C. G. // Journal of the London Mathematical Society;10/01/1999, Vol. 60 Issue 2, p630

A new coupling of one-dimensional random walks is described which tries to control the coupling by keeping the separation of the two random walks of constant sign. It turns out that among such monotone couplings there is an optimal one-step coupling which maximises the second moment of the...

• The influence of the first term of an arithmetic progression. Fiorilli, Daniel // Proceedings of the London Mathematical Society;Apr2013, Vol. 106 Issue 4, p819

The goal of this paper is to study the discrepancy of the distribution of arithmetic sequences in arithmetic progressions. We will fix a sequence î” ={a(n)}nâ‰¥1 of non-negative real numbers in a certain class of arithmetic sequences. For a fixed integer aâ‰ 0, we will be interested...

• Applying spartan to Understand Parameter Uncertainty in Simulations. Alden, Kieran; Read, Mark; Andrews, Paul S.; Timmis, Jon; Coles, Mark // R Journal;Dec2014, Vol. 6 Issue 2, p63

In attempts to further understand the dynamics of complex systems, the application of computer simulation is becoming increasingly prevalent. Whereas a great deal of focus has been placed in the development of software tools that aid researchers develop simulations, similar focus has not been...

• Limit theorems in the theory of discrete periodic splines. Malozemov, V. N.; Chashnikov, N. V. // Doklady Mathematics;Feb2011, Vol. 83 Issue 1, p39

The article presents a mathematical problem and equation on limit theorems based on discreet periodic splines theory. It explains the double limits theorem where any real number x and integer n are equal to each other. It presents the case where the double limit is calculated in a reverse order...

• Asymptotic behavior of higher-order neutral difference equations with general arguments. Chatzarakis, G.; Khatibzadeh, H.; Miliaras, G.; Stavroulakis, I. // Ukrainian Mathematical Journal;Aug2013, Vol. 65 Issue 3, p478

We study the asymptotic behavior of solutions of the higher-order neutral difference equation where Ï„ ( n) is a general retarded argument, Ïƒ( n) is a general deviated argument, c âˆˆ \$ \mathbb{R} \$; ( p( n)) is a sequence of real numbers, âˆ† denotes the forward difference operator...

• Maximal Monotone Operators and the Proximal Point Algorithm in the Presence of Computational Errors. Zaslavski, A. J. // Journal of Optimization Theory & Applications;Jul2011, Vol. 150 Issue 1, p20

In a finite-dimensional Euclidean space, we study the convergence of a proximal point method to a solution of the inclusion induced by a maximal monotone operator, under the presence of computational errors. Most results known in the literature establish the convergence of proximal point...

• The Weighted Hardy Inequality: New Proofs and the Case p = 1. Sinnamon, Gord; Stepanov, Vladimir D. // Journal of the London Mathematical Society;1996, Vol. 54 Issue 1, p89

An elementary proof is given of the weight characterisation for the Hardy inequality (âˆ«0âˆž(âˆ«0âˆžf)qÏ…(x)dx)1/q â‰¤C (âˆ«0âˆžfpu)1/p for fâ‰¥0, (1.1) in the case 0 < q < p, 1 < p < âˆž. It is also shown that certain weighted inequalities with monotone kernels...

Share