The following list is based
on the bibliography compiled in the Selecta of William Feller
Selected Papers (2 vol) edited by R.
Schilling, Z. Vondraček and W. Woyczyński (Springer, Cham 2015)
. The DOIs and Links provided give access to the relevant publication as
long
as your IP-Number has access rights (e.g. by subscription to the
relevant journal or archive).
- Über algebraisch rektifizierbare transzendente Kurven [On algebraically rectifiable transcendental curves].
PhD-Thesis Universität Göttingen, June 1926. Advisor: Richard Courant. Also published as [2]
Google books
- Über algebraisch rektifizierbare transzendente
Kurven [On algebraically rectifiable transcendental curves].
Mathematische Zeitschrift 27 (1928) 481-495.
DOI: 10.1007/BF01171108
- Über die Lösungen der linearen partiellen Differentialgleichungen zweiter Ordnung vom elliptischen Typus [On the solutions of second-order
linear partial differential equations of elliptic type].
Habilitationsschrift Universität Kiel, February 1929. Also published as [4]
- Über die Lösungen der linearen
partiellen Differentialgleichungen zweiter Ordnung vom elliptischen
Typus [On the solutions of second-order
linear partial differential equations of elliptic type].
Mathematische Annalen 102 (1930) 633-649.
DOI: 10.1007/BF01782367
- (with Erhard Tornier) Mengentheoretische Untersuchung von
Eigenschaften der Zahlenreihe [Set-theoretic investigation of some
properties of the natural numbers].
Zentralblatt 1 (1931) 257–259.
- (with Erhard Tornier) Maß- und Inhaltstheorie des
Baireschen Nullraumes [Measure and integration theory of Baire’s
null space].
Mathematische Annalen 107 (1932) 165–187.
DOI: http://dx.doi.org/10.1007/BF01448889
- (with Erhard Tornier) Mengentheoretische Untersuchung von
Eigenschaften der Zahlenreihe [Set-theoretic investigation of some
properties of
the natural numbers].
Mathematische Annalen 107 (1932) 188–232.
DOI: http://dx.doi.org/10.1007/BF01448890
- Allgemeine Maßtheorie und Lebesguesche Integration [General measure theory and Lebesgue integration].
Sitzungsberichte der Preußischen Akademie derWissenschaften, Physikalisch–Mathematische Klasse 27 (1932) 459–472.
- (with Herbert Busemann) Zur Differentiation der
Lebesgueschen Integrale [On the differentiation of Lebesgue’s integrals].
Fundamenta Mathematicae 22 (1934) 226-256.
Link
to the journal
- Bemerkungen zur Maßtheorie in abstrakten Räumen [Remarks on measure theory in abstract spaces].
Bulletin international de
l’académie Yougoslave des sciences et des beaux-arts,
Zagreb. Classe des sciences mathématiques et naturelles 28 (1934) 30–45.
Croatian original publication: Dr. Vilim (W.) Feller: Prilog teoriji mjera u apstraktnim prostorima. RAD 249 (1934) 204–224.
- (with Herbert Busemann) Bemerkungen zur Differentialgeometrie der
konvexen Flächen. I. Kürzeste Linien auf differenzierbaren
Flächen [Remarks
on the differential geometry of convex surfaces. I. Shortest lines on differentiable surfaces].
Matematisk Tidsskrift B (1935) 25–36.
- (with Herbert Busemann) Bemerkungen zur Differentialgeometrie der
konvexen Flächen. II. Über die Krümmungsindikatrizen
[Remarks on
the differential geometry of convex surfaces. II. On curvature indicatrices].
Matematisk Tidsskrift B (1935) 87–115.
- Über den zentralen Grenzwertsatz der
Wahrscheinlichkeitsrechnung [On the central limit theorem of probability theory].
Mathematische Zeitschrift 40 (1936) 521-559.
DOI: 10.1007/BF01218878
- (with Herbert Busemann) Bemerkungen zur Differentialgeometrie der
konvexen Flächen. III. Über die Gauss’sche
Krümmung [Remarks on the
differential geometry of convex surfaces. III. On Gauss’ curvature].
Matematisk Tidsskrift B (1936) 41–70.
- (with Herbert Busemann) Krümmungseigenschaften
konvexer Flächen.[Curvature properties of convex surfaces]
Acta Mathematica 66 (1936) 1-47.
DOI: 10.1007/BF02546515
- Zur Theorie der stochastischen Prozesse. (Existenz- und
Eindeutigkeitssätze). [On the theory of stochastic processes. (Existence and Uniqueness theorems)].
Mathematische Annalen 113 (1936) 113-160.
DOI: 10.1007/BF01571626
- Über den zentralen Grenzwertsatz der
Wahrscheinlichkeitsrechnung. II [On the central limit theorem of probability theory. II].
Mathematische Zeitschrift 42 (1937) 301-312.
DOI: 10.1007/BF01160080
Erratum. Mathematische Zeitschrift 44 (1939) 794.
DOI: 10.1007/BF01210684
- Über das Gesetz der großen Zahlen [On the law of large numbers].
Acta
Litterarum ac Scientiarum. Regiae Universitatis Hungaricae
Francisco-Josephinae. Sectio Scientiarum Mathematicarum. (Acta. Sci.
Litt. Szeged) 8 (1937) 191-201.
Link to
the journal
- Über die Theorie der stochastischen Prozesse [On the theory of stochastic processes].
In: Comptes Rendus du Congrès International des Mathématiciens. Oslo 1936. Vol. 2. A. W. Brøggers Boktrykkeri A/S, Oslo 1937, pp. 194–196.
- Sur les axiomatiques du calcul des probabilités et leurs
relations avec les expériences [On the axioms of probability
theory and their relations with
the experience].
In: P. Cantelli, M. Fréchet, R. von Mises, I. F. Steffensen and A.Wald (eds.): Conférences internationales de sciences mathématiques.
Colloque consacré à la théorie des probabilités. II: Les fondements du calcul des probabilités.
Actualités scientifiques et industrielles 735. Hermann & Cie., Paris 1938, pp. 7–21.
- Note on regions similar to the sample space.
Statistical Research Memoirs, University College London 2 (1938), 117–125.
- (with J. Runnström and E. Sperber) Die Aufnahme von Glucose
durch Bäckerhefe unter aeroben und anaeroben Bedingungen [On the
absorption
of glucose by baker’s yeast under aerobic and anaerobic conditions].
Naturwissenschaften 26 (1938) 547–548.
- Die Grundlagen der Volterraschen Theorie des Kampfes ums
Dasein in wahrscheinlichkeitstheoretischer Behandlung [The foundations of
Volterra’s theory on the struggle for life in a probabilistic treatment].
Acta Biotheoretica, Leiden 5 (1939) 11-39.
DOI: 10.1007/BF01602932
- Completely monotone functions and sequences.
Duke Mathematical Journal 5 (1939) 661-674.
DOI: 10.1215/S0012-7094-39-00555-7
- Über die Existenz von sogenannten Kollektiven [On the existence of so-called Kollektivs].
Fundamenta Mathematicae 32 (1939) 87-96.
Link
to the journal
- Neuer Beweis für die Kolmogoroff-P.
Lévysche
Charakterisierung der unbeschränkt teilbaren
Verteilungsfunktionen [A new proof of Kolmogoroff’s and P.
Levy’s characterization of infinitely divisible distribution
functions].
Bulletin
international de l'académie Yougoslave des sciences et des
beaux-arts,
Zagreb. Classe des sciences mathématiques et naturelles
32 (1939) 106-113.
- On the logistic law of growth and its empirical verifications in biology.
Acta Biotheoretica, Leiden 5 (1940) 51–65.
DOI: http://dx.doi.org/10.1007/BF01602862
- On the time distribution of so-called random events.
Physical Reviews, II. Series 57 (1940) 906–908.
DOI: http://dx.doi.org/10.1103/PhysRev.57.906
- On the integro-differential equations of purely
discontinuous Markoff processes.
Transactions of the American Mathematical Society
48 (1940) 488-515.
DOI: 10.1090/S0002-9947-1940-0002697-3
- Statistical aspects of ESP.
Journal of Parapsychology 4 (1940) 271–298.
Link to the journal
- On the integral equation of renewal theory.
Annals of Mathematical Statistics 12 (1941)
243-267.
DOI: 10.1214/aoms/1177731708
- (with Jacob David Tamarkin) Partial Differential Equations.
Brown University Summer Session for Advanced Instructions &
Research in Mechanics. 6/23- 9/13 1941, Providence (RI) 1941. Chapters
1–3 by J. D. Tamarkin, Chapters 4–7 by William Feller.
Reprinted by the Lewis Flight Propulsion Laboratory, National Committee for Aeronautics, Cleveland 1956.
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- Some geometric inequalities.
Duke Mathematical Journal 9 (1942) 885-892.
DOI: 10.1215/S0012-7094-42-00963-3
- On A. C. Aitken’s method of interpolation.
Quarterly of Applied Mathematics 1 (1943) 86–87.
Link to the journal
- Generalization of a probability limit theorem of
Cramér.
Transactions of the American Mathematical Society
54 (1943) 361-372.
DOI: 10.1090/S0002-9947-1943-0009262-5
- The general form of the so-called law of the iterated
logarithm.
Transactions of the American Mathematical Society
54 (1943) 373-402.
DOI: 10.1090/S0002-9947-1943-0009263-7
- On a general class of "contagious" distributions.
Annals of Mathematical Statistics 14 (1943)
389-400.
DOI: 10.1214/aoms/1177731359
- On the normal approximation to the binomial distribution.
Annals of Mathematical Statistics 16 (1945)
319-329.
DOI: 10.1214/aoms/1177731058
- The fundamental limit theorems in probability.
Bulletin of the American Mathematical Society
51 (1945) 800-832.
DOI: 10.1090/S0002-9904-1945-08448-1
- (with Herbert Busemann) Regularity properties of a certain
class of surfaces.
Bulletin of the American Mathematical Society
51 (1945) 583-598.
DOI: 10.1090/S0002-9904-1945-08403-1
- Note on the law of large numbers and "fair" games.
Annals of Mathematical Statistics 16 (1945)
301-304.
DOI: 10.1214/aoms/1177731094
- A limit theorem for random variables with infinite moments.
American Journal of Mathematics 68 (1946)
257-262.
DOI: 10.2307/2371837
- The law of the iterated logarithm for identically
distributed random variables.
Annals of Mathematics 47 (1946) 631-638.
DOI: 10.2307/1969225
- On the Kolmogorov-Smirnov limit theorems for empirical
distributions.
Annals of Mathematical Statistics 19 (1948)
177-189.
DOI: 10.1214/aoms/1177730243
Erratum. Annals of Mathematical Statistics 21 (1950)
301-302.
DOI: 10.1214/aoms/1177729850
- Spanish Translation of the paper [40]
Revista Matemática Hispano-Americana, IV. Seria 8 (1948) 95–132.
- On probability problems in the theory of counters.
In: Studies, Essays, presented to R. Courant (Courant
anniversary volume) Interscience Publishers, New York 1948,
pp. 105-115.
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- (with Paul Erdös and Harry Pollard) A property of
power series with positive coefficients.
Bulletin of the American Mathematical Society
55 (1949) 201-204.
DOI: 10.1090/S0002-9904-1949-09203-0
- (with Kai Lai Chung) On fluctuations in coin-tossing.
Proceedings of the National Academy of Sciences, USA
35 (1949) 605-608.
DOI: 10.1073/pnas.35.10.605
- On the theory of stochastic processes, with particular
reference to applications.
In: J. Neyman (ed.): Proceedings of the (First) Berkeley
Symposium on Mathematical Statistics and Probability 1945/46.
University of California Press, Berkeley, Los Angeles 1949, pp. 403-432.
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Euclid
- Fluctuation theory of recurrent events.
Transactions of the American Mathematical Society
67 (1949) 98-119.
DOI: 10.1090/S0002-9947-1949-0032114-7
- An Introduction to Probability Theory and Its Applications.
John Wiley & Sons, New York 1950.
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- The asymptotic distribution of the range of sums of
independent random variables.
Annals of Mathematical Statistics 22 (1951)
427-432.
DOI: 10.1214/aoms/1177729589
- (with George E. Forsythe) New matrix transformations for obtaining characteristic vectors.
Quarterly of Applied Mathematics 8 (1951) 325–331.
Link to the journal
- The problem of n liars and Markov chains.
American Mathematical Monthly 58 (1951) 606–608.
DOI: http://dx.doi.org/10.2307/2306351
- Diffusion processes in genetics.
In: J. Neyman (ed.): Proceedings of the Second Berkeley
Symposium on Mathematical Statistics and Probability 1950.
University of California Press, Berkeley, Los Angeles (CA) 1951, pp.
227-246.
Project Euclid
- Two singular diffusion problems.
Annals of Mathematics 54 (1951) 173-182.
DOI: 10.2307/1969318
- The parabolic differential equations and the associated
semigroups of transformation.
Annals of Mathematics 55 (1952) 468-519.
DOI: 10.2307/1969644
- On a generalization of Marcel Riesz' potentials and the
semigroups generated by them.
In: Meddelanden från Lunds Universitets
Matematiska Seminarium. Supplement M. Riesz, Uppsala 1952,
pp. 73-81.
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Books
- Some recent trends in the mathematical theory of diffusion.
In: Proceedings of the International Congress of
Mathematicians, Cambridge (MA) 1950. Vol. 2. American
Mathematical Society, Providence (RI) 1952, pp. 322-339.
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- (with George E. Forsythe) New matrix transformations for obtaining characteristic vectors.
In: Proceedings of the International Congress of Mathematicians, Cambridge (MA) 1950. Vol. 1. American Mathematical Society, Providence (RI) 1952, p. 661.
- On positivity preserving semigroups of transformations on
C[r1,r2].
Annales de la Société Polonaise de
Mathématique 25 (1952) 85-94.
Link
to the journal
- Semigroups of transformations in general weak topologies.
Annals of Mathematics 57 (1953) 287-308.
DOI: 10.2307/1969859
- On the generation of unbounded semigroups of bounded linear
operators.
Annals of Mathematics 58 (1953) 166-174.
DOI: 10.2307/1969826
- The general diffusion operator and positivity preserving
semigroups in one dimension.
Annals of Mathematics 60 (1954) 417-436.
DOI: 10.2307/1969842
- Diffusion processes in one dimension.
Transactions of the American Mathematical Society
77 (1954) 1-31.
DOI: 10.1090/S0002-9947-1954-0063607-6
- On second order differential operators.
Annals of Mathematics 61 (1955) 90-105.
DOI: 10.2307/1969621
- On differential operators and boundary conditions.
Communications on Pure and Applied Mathematics
8 (1955) 203-216.
DOI: 10.1002/cpa.3160080112
- Boundaries induced by non-negative matrices.
Transactions of the American Mathematical Society
83 (1956) 19-54.
DOI: 10.1090/S0002-9947-1956-0090927-3
- (with Henry P. McKean Jr.) A diffusion equivalent to a
countable Markov chain.
Proceedings of the National Academy of Sciences, USA
42 (1956) 351-354.
DOI: 10.1073/pnas.42.6.351
- (with Joanne Elliott) Stochastic processes connected with
harmonic functions.
Transactions of the American Mathematical Society
82 (1956) 392-420.
DOI: 10.1090/S0002-9947-1956-0086440-X
- On generalized Sturm–Liouville operators.
In: J. B. Diaz and L. E. Payne (eds.): Proceedings of the Conference on Differential Equations (Dedicated to A. Weinstein), University of Maryland Book Store, College Park (MD) 1956, pp. 251–270.
- Generalized second order differential operators and their
lateral conditions.
Illinois Journal of Mathematics 1 (1957)
459-504.
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- The numbers of zeros and of changes of sign in a symmetric random walk.
L’Enseignement Mathématique, IIe. Série 3 (1957) 229–235.
- Sur une forme intrinsèque pour les opérateurs
différentiels du second ordre [On an intrinsic form of
second-order differential operators].
Publications de l’Institut
de Statistique de l’Université de Paris. Université
de Paris VI, Institut de Statistique, Paris 6 (1957) 291–301.
- On boundaries and lateral conditions for the Kolmogorov
differential equations.
Annals of Mathematics 65 (1957) 527-570.
DOI: 10.2307/1970064
Additional notes. Annals of Mathematics 68 (1958) 735-736.
DOI: 10.2307/1970166
- On boundaries defined by stochastic matrices.
In: Proceedings of Symposia in Applied Mathematics.
Vol. 7. McGraw-Hill Book Co., New York (for the American Mathematical
Society, Providence (RI)) 1957, 35-40.
DOI: 10.1090/psapm/007
- An Introduction to Probability Theory and Its Applications. Vol. 1.
2nd edn. of [51]. John Wiley & Sons, New York 1957.
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- On the intrinsic form for second order differential
operators.
Illinois Journal of Mathematics 2 (1958) 1-18.
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- On combinatorial methods in fluctuation theory.
In: U. Grenander (ed.): The Harald Cramér Volume. Almqvist & Wiksell, Stockholm; John Wiley & Sons, New York 1959, pp. 75–91.
- The birth and death processes as diffusion processes.
Journal de Mathématiques pures et
appliquées, IX. série 38 (1959)
301-345.
Link to the journal
- Non-Markovian processes with the semigroup property.
Annals of Mathematical Statistics 30 (1959)
1252-1253.
DOI: 10.1214/aoms/1177706110
- Differential operators with the positive maximum property.
Illinois Journal of Mathematics 3 (1959)
182-186.
Project Euclid
- On the equation of the vibrating string.
Journal of Mathematics and Mechanics 8 (1959) 339–348.
DOI: http://dx.doi.org/10.1512/iumj.1959.8.58023
- Some new connections between probability and classical
analysis.
Proceedings of the International Congress of
Mathematicians, Edinburgh 1958. Cambridge University Press,
Cambridge 1960, pp. 69-86.
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- (with Steven Orey) A renewal theorem.
Journal of Mathematics and Mechanics 10 (1961)
619-624.
DOI: 10.1512/iumj.1961.10.10041
- A simple proof for renewal theorems.
Communications on Pure and Applied Mathematics
14 (1961) 285-293.
DOI: 10.1002/cpa.3160140308
- Chance processes and fluctuations.
In: E. F. Beckenbach and M. R. Hestenes (eds.): Modern Mathematics for the Engineer: Second Series. University of California Engineering Extension Series. Mc Graw-Hill, New York 1961, pp. 167–181.
- On the classical Tauberian theorems.
Archiv der Mathematik 14 (1963) 317-322.
DOI: 10.1007/BF01234960
- On semi-Markov processes.
Proceedings of the National Academy of Sciences, USA
51 (1964) 653-659.
DOI: 10.1073/pnas.51.4.653
- On the Fourier representation for Markov chains and the
strong ratio theorem.
Journal of Mathematics and Mechanics 15 (1966)
273-283.
DOI: 10.1512/iumj.1966.15.15019
- On the influence of natural selection on population size.
Proceedings of the National Academy of Sciences, USA
55 (1966) 733-738.
DOI: 10.1073/pnas.55.4.733
- Infinitely divisible distributions and Bessel functions
associated with random walks.
SIAM Journal of Applied Mathematics 14 (1966)
864-875.
DOI: 10.1137/0114071
- An Introduction to Probability Theory and Its Applications. Vol. 2.
John Wiley & Sons, New York 1966.
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- On regular variation and local limit theorems.
In: J. Neyman and L. LeCam (eds.): Proceedings of the Fifth
Berkeley Symposium on Mathematical Statistics and Probability 1965/66,
Vol. 2, Pt. 1, University of California Press, Berkeley, Los Angeles
(Ca) 1967, pp. 373-388.
Project Euclid
- A direct proof of Stirling’s formula.
American Mathematical Monthly 74 (1967) 1223–1225.
DOI: http://dx.doi.org/10.2307/2315671
Erratum: American Mathematical Monthly 75 (1968) 518.
DOI: http://dx.doi.org/10.2307/2314719
- On fitness and the cost of natural selection.
Genetics Research 9 (1967) 1-15.
DOI: 10.1017/S0016672300010260
- On Müntz’ theorem and completely monotone functions.
American Mathematical Monthly 75 (1968) 342–350.
DOI: http://dx.doi.org/10.2307/2313410
- On the Berry-Esseen theorem.
Zeitschrift für Wahrscheinlichkeitstheorie und
verwandte Gebiete 10 (1968) 261-268.
DOI: 10.1007/BF00536279
- On probabilities of large deviations.
Proceedings of the National Academy of Sciences, USA 61 (1968) 1224–1227.
DOI: http://dx.doi.org/10.1073/pnas.61.4.1224
- An extension of the law of the iterated logarithm to
variables without variance.
Journal of Mathematics and Mechanics 18 (1968)
343-355.
DOI: 10.1512/iumj.1969.18.18027
- An Introduction to Probability Theory and Its Applications. Vol. 1.
3rd edn. of [51], [77]. John Wiley & Sons, New York 1968.
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- A geometrical analysis of fitness in triply allelic systems.
Mathematical Biosciences 5 (1969) 19–38.
DOI: http://dx.doi.org/10.1016/0025-5564(69)90033-9
- One-sided analogues of Karamata's regular variation.
L'Enseignement Mathématique, IIe. Serie
15 (1969) 107-121.
DOI: 10.5169/seals-43209
- Limit theorems for probabilities of large deviations.
Zeitschrift für Wahrscheinlichkeitstheorie und
verwandte Gebiete 14 (1969) 1-20.
DOI: 10.1007/BF00534113
- General analogues to the law of the iterated logarithm.
Zeitschrift für Wahrscheinlichkeitstheorie und
verwandte Gebiete 14 (1969) 21-26.
DOI: 10.1007/BF00534114
- On the fluctuations of sums of independent random variables.
Proceedings of the National Academy of Sciences, USA 63 (1969) 637–639.
DOI: http://dx.doi.org/10.1073/pnas.63.3.637
- Are life scientists overawed by Statistics? (Too much faith in statistics).
Scientific Research 4.3 (1969) 24–29.
- On the oscillations of sums of independent random variables.
Annals of Mathematics 91 (1970) 402-418.
DOI: 10.2307/1970583
- An Introduction to Probability Theory and Its Applications. Vol. 2.
2nd edn. of [93]. John Wiley & Sons, New York 1971. Posthumously
published. The final version was published with the help of J. Goldman,
A. Grunbaum, H. P. McKean, L. Pitt and A. Pittenger.
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