Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/wiley/g-h-hardy-and-probability-JR7LsQD8Qa
References (84)
-
J. Kahane (1985)
Some Random Series of Functions -
M. Kac (1959)
Statistical Independence in Probability Analysis and Number Theory -
J. Littlewood (1969)
On the probability in the tail of a binomial distributionAdvances in Applied Probability, 1
-
P. Koosis (1999)
Introduction to H[p] spaces -
Jun Liu (2001)
Monte Carlo strategies in scientific computing -
A. Hildebrand (1986)
The prime number theorem via the large sieveMathematika, 33
-
H. Mann (1963)
Statistical Independence in Probability, Analysis and Number Theory (M. Kac)Siam Review, 5
-
P. Diaconis, F. Mosteller, H. Onishi (1977)
Second-order terms for the variances and covariances of the number of prime factors—Including the square free case ☆Journal of Number Theory, 9
-
R. Bass (1997)
Diffusions and Elliptic Operators -
P. Elliott (1984)
Arithmetic Functions and Integer Products -
P. Duren (1970)
Theory of H[p] spaces -
O. Kellogg (1934)
Foundations of potential theoryThe Mathematical Gazette, 18
-
David Williams (1991)
Probability with Martingales -
G. Hardy, J. Littlewood (1930)
A maximal theorem with function-theoretic applicationsActa Mathematica, 54
-
T. Hesterberg (2002)
Monte Carlo Strategies in Scientific ComputingTechnometrics, 44
-
E. Stein, G. Weiss (1971)
Introduction to Fourier Analysis on Euclidean Spaces. -
L. Miclo (1999)
An example of application of discrete Hardy''s inequalities -
(1958)
Espaces de Dirichlet I, le cas elementaire -
S. Axler, P. Bourdon, W. Ramey (1992)
Harmonic Function Theory -
E. T. (1946)
An Introduction to the Theory of NumbersNature, 157
-
P. Diaconis, C. Stein (1978)
Some Tauberian Theorems Related to Coin TossingAnnals of Probability, 6
-
M. Kac, P. Andersen (1986)
Enigmas of Chance: An AutobiographyPhysics Today, 41
-
N. Varopoulos (1980)
The Helson-Szegö theorem and Ap-functions for Brownian motion and several variablesJournal of Functional Analysis, 39
-
(1999)
Martingales and Brownian motion, 3rd edn (Springer -
(1994)
Dirichlet forms and symmetric Markov processes -
M. Brelot (1986)
Classical potential theory and its probabilistic counterpartMetrika, 33
-
(1928)
Notes on some points in the integral calculus LXIV: further inequalities between integrals -
P. Diaconis (1980)
Average Running Time of the Fast Fourier TransformJ. Algorithms, 1
-
R. Bañuelos, C. Moore (1999)
Probabilistic behavior of harmonic functions -
E. Davies (1998)
A review of Hardy inequalitiesOperator theory, 110
-
P. Erdös (1942)
On the Law of the Iterated LogarithmAnnals of Mathematics, 43
-
D. Knuth (2000)
Selected papers on analysis of algorithms, 102
-
F. Delbaen, W. Schachermayer (1999)
A compactness principle for bounded sequences of martingales with applications -
(1971)
An introduction to probability and its application 2, 2nd edn (Wiley -
M.
A Course of Pure MathematicsNature, 80
-
G. Hardy, By Hardy (1939)
An Introduction to the Theory of NumbersThe Mathematical Gazette, 23
-
L. Saloff‐Coste (1997)
Lectures on finite Markov chains -
D. Knuth (1981)
The Art of Computer Programming, Vol. 2 -
F. Mosteller (1972)
A data-analytic look at Goldbach countsStatistica Neerlandica, 26
-
Peter Mörters, Yuval Peres (2010)
Brownian Motion: Hausdorff dimension: Techniques and applications -
(1949)
Divergent series (Oxford -
J. Kingman, J. Neveu (1973)
Martingales à temps discret, 136
-
S. Kakutani (1944)
143. Two-dimensional Brownian Motion and Harmonic Functions, 20
-
R. Vaughan (1981)
The Hardy-Littlewood Method -
(1966)
I (Edited by a committee appointed by the London Math -
J. Doob (1954)
Semimartingales and subharmonic functionsTransactions of the American Mathematical Society, 77
-
Two . dimensional Brownian Motion and Harmonic Functions -
S. Zabell (1995)
ALAN TURING AND THE CENTRAL LIMIT THEOREMAmerican Mathematical Monthly, 102
-
R. Bass (1994)
Probabilistic Techniques in Analysis -
Burgess Davis (1975)
Picard’s theorem and Brownian motionTransactions of the American Mathematical Society, 213
-
T. Lai (1973)
Optimal Stopping and Sequential Tests which Minimize the Maximum Expected Sample SizeAnnals of Statistics, 1
-
C. Fefferman, C. Fefferman, E. Stein, E. Stein (1972)
Hp spaces of several variablesActa Mathematica, 129
-
L. Sathe (1954)
On a Problem of Hardy on the Distribution of Integers having a Given Number of Prime Factors IIIJournal of the Indian Mathematical Society, 18
-
Z. Nehari (1950)
Bounded analytic functionsBulletin of the American Mathematical Society, 57
-
G. Hardy (1922)
The Theory of NumbersNature, 110
-
J. Gall (1999)
Spatial Branching Processes, Random Snakes, and Partial Differential Equations -
P. Diaconis (1977)
Examples for the Theory of Infinite Iteration of Summability MethodsCanadian Journal of Mathematics, 29
-
Dr. Záruba (2018)
Stochastic ProcessesGauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics
-
D. Kramkov (1996)
Optional decomposition of supermartingales and hedging contingent claims in incomplete security marketsProbability Theory and Related Fields, 105
-
D. Knuth (1970)
The Art of Computer Programming, Volume II: Seminumerical Algorithms -
R. Raimi (1976)
The First Digit ProblemAmerican Mathematical Monthly, 83
-
P. Elliott (1979)
Probabilistic number theory -
D. Burkholder, R. Gundy, M. Silverstein (1971)
A maximal function characterization of the classTransactions of the American Mathematical Society, 157
-
J. Burkill, J. Littlewood (1954)
A mathematician's miscellanyThe Mathematical Gazette, 38
-
N. Bingham (1986)
Variants on the Law of the Iterated LogarithmBulletin of The London Mathematical Society, 18
-
(1999)
Convergence of probability measures, 2nd edn (Wiley -
P. Donnelly (1987)
MARKOV PROCESSES Characterization and Convergence (Wiley Series in Probability and Mathematical Statistics)Bulletin of The London Mathematical Society, 19
-
P. Erdös, M. Kac (1940)
The Gaussian Law of Errors in the Theory of Additive Number Theoretic FunctionsAmerican Journal of Mathematics, 62
-
L. Carleson (1962)
Interpolations by Bounded Analytic Functions and the Corona ProblemAnnals of Mathematics, 76
-
(1952)
Pólya, Inequalities, 2nd edn -
T. Hill (1995)
A Statistical Derivation of the Significant-Digit LawStatistical Science, 10
-
L. Dickson (1933)
Introduction to the theory of numbersThe Mathematical Gazette, 17
-
A. Khintchine (1923)
Über dyadische BrücheMathematische Zeitschrift, 18
-
P. Diaconis (1977)
The Distribution of Leading Digits and Uniform Distribution Mod 1Annals of Probability, 5
-
M. Borel (1909)
Les probabilités dénombrables et leurs applications arithmétiquesRendiconti Del Circolo Matematico Di Palermo, 27
-
R. Durrett (1984)
Brownian motion and martingales in analysis -
P. Meyer (1966)
Probability and potentials -
G. Tenenbaum (1995)
Introduction to Analytic and Probabilistic Number Theory -
Y. Meyer (1993)
Wavelets and Operators -
F. S. (1941)
A Mathematician's ApologyNature, 147
-
(1983)
Probabilités et potentiel: théorie discrète du potentiel (Hermann, Paris, 1983) -
B. Flehinger (1966)
On the Probability that a Random Integer has Initial Digit AAmerican Mathematical Monthly, 73
-
P. Turán (1934)
On a Theorem of Hardy and RamanujanJournal of The London Mathematical Society-second Series
-
G. Hardy
The Mean Value of the Modulus of an Analytic FunctionProceedings of The London Mathematical Society
- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/S002460930200111X
- Publisher site
- See Article on Publisher Site
Abstract
Despite a true antipathy to the subject, Hardy contributed deeply to modern probability. His work with Ramanujan begat probabilistic number theory. His work on Tauberian theorems and divergent series has probabilistic proofs and interpretations. Finally, Hardy spaces are a central ingredient in stochastic calculus. This paper reviews his prejudices and accomplishments, through these examples. 2000 Mathematics Subject Classification 60‐02, 11K65, 40E05.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Jul 1, 2002