Chung Kai-lai | Academic Influence

Chung Kai-lai's AcademicInfluence.com Rankings

Chung Kai-lai

Mathematics

#1355

World Rank

#2253

Historical Rank

#562

USA Rank

Measure Theory

#143

World Rank

#225

Historical Rank

#63

USA Rank

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Mathematics

Chung Kai-lai's Degrees

PhD Mathematics University of California, Berkeley
Masters Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Chung Kai-lai Influential?

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According to Wikipedia, Kai Lai Chung was a Chinese-American mathematician known for his significant contributions to modern probability theory. Biography Chung was a native of Hangzhou, the capital city of Zhejiang Province. Chung entered Tsinghua University in 1936, and initially studied physics at its Department of Physics. In 1940, Chung graduated from the Department of Mathematics of the National Southwestern Associated University, where he later worked as a teaching assistant. During this period, he first studied number theory with Lo-Keng Hua and then probability theory with Pao-Lu Hsu.

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Chung Kai-lai's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

A Course in Probability Theory (1949) (2733)
Markov Chains with Stationary Transition Probabilities (1961) (1517)
From Brownian Motion To Schrödinger's Equation (1995) (582)
Lectures from Markov processes to Brownian motion (1982) (249)
On a Stochastic Approximation Method (1954) (238)
Markov Processes, Brownian Motion, and Time Symmetry (2005) (215)
On the distribution of values of sums of random variables (1951) (208)
Elementary Probability Theory with Stochastic Processes. (1975) (206)
Excursions in Brownian motion (1976) (204)
An estimate concerning the Kolmogoroff limit distribution (1949) (165)
Review: William Feller, An Introduction to Probability Theory and its Applications 2 (1973) (156)
On fluctuations in coin tossing. (1949) (132)
On the application of the borel-cantelli lemma (1952) (132)
On the maximum partial sums of sequences of independent random variables (1948) (102)
A Note on the Ergodic Theorem of Information Theory (1961) (102)
Probabilistic approach in potential theory to the equilibrium problem (1973) (67)
Doubly-Feller Process with Multiplicative Functional (1986) (61)
To reverse a Markov process (1969) (58)
Introduction to Random Time and Quantum Randomness (2003) (56)
PROBABILITY AND POTENTIAL (1995) (54)
On the Lipschitz's condition for Brownian motion (1959) (51)
Note on Some Strong Laws of Large Numbers (1947) (50)
Feynman-Kac Functional and the Schrödinger Equation (1981) (50)
FIELDS, OPTIONALITY AND MEASURABILITY.* (1965) (49)
The Strong Law of Large Numbers (1951) (48)
The Approximate Distribution of Student's Statistic (1946) (43)
MATHEMATICS AND APPLICATIONS (2004) (43)
Book Review — An Introduction to Probability Theory and its Applications 2, 2nd ed. (2004) (40)
Contributions to the theory of Markov chains. II (1954) (35)
On the Zeros of ∑\limits n 1 ± 1 (1949) (35)
The general theory of Markov processes according to Doeblin (1964) (34)
Elementary probability theory : with stochastic processes and an introduction to mathematical finance (2003) (33)
Stochastic Stability and Control, Mathematics in Science and Engineering (1972) (32)
The lifetime of conditional brownian motion in the plane (1984) (29)
General gauge theorem for multiplicative functionals (1988) (28)
On the boundary theory for Markov chains. II (1963) (27)
Lectures on Boundary Theory for Markov Chains. (1970) (27)
Meyer's theorem on predictability (1974) (26)
On a Limit Theorem in Renewal Theory (1952) (24)
Maxima in Brownian excursions (1975) (23)
Elementary Probability Theory (1974) (23)
Contributions to the theory of Markov chains (1953) (23)
A new setting for potential theory. I (1980) (21)
On the recurrence of sums of random variables (1962) (21)
The Condenser Problem (1977) (21)
Asymptotic distribution of the maximum cumulative sum of independent random variables (1948) (21)
On the Exponential Formulas of Semi-Group Theory. (1962) (21)
On the Probability of the Occurrence of at Least $m$ Events Among $n$ Arbitrary Events (1941) (20)
On Mutually Favorable Events (1942) (20)
Probability limit theorems assuming only the first moment (2008) (18)
An extension of renewal theory (1952) (17)
Green, Brown, and Probability (1995) (17)
Left continuous moderate Markov processes (1979) (16)
Downcrossings and local time (1976) (16)
Task analysis for computer-aided design (CAD) at a keystroke level. (1996) (16)
Seminar on Stochastic Processes, 1992 (1993) (15)
On the lower limit of sums of independent random variables (1947) (15)
Greenian bounds for Markov processes (1992) (15)
Emptiness times of a dam with stable input and general release function (1975) (14)
The generating function (1960) (14)
Absolute Moments and Characteristic Function (1983) (13)
Kac functional and Schrödinger equation (1980) (13)
Some new developments in Markov chains (1956) (12)
The Poisson process as renewal process (1972) (12)
Foundations of the Theory of Continuous Parameter Markov Chains (1956) (12)
A cluster of great formulas (1982) (11)
FLUCTUATIONS OF SUMS OF INDEPENDENT RANDOM VARIABLES (1950) (11)
Green, Brown, and probability & Brownian motion on the line (1982) (11)
The gauge and conditional gauge theorem (1985) (9)
Four papers on probability (1951) (9)
Green's function for a ball (1986) (8)
On the Maximum Partial Sum of Independent Random Variables. (1947) (8)
On stopped feynman-KAC functionals (1980) (8)
A Combinatorial Formula and its Application to the Theory of Probability of Arbitrary Events (1945) (7)
Non-recurrent random walks. (1956) (7)
Seminar on Stochastic Processes, 1981 (1982) (7)
Seminar on Stochastic Processes, 1986 (1987) (7)
Option Pricing Theory (2003) (7)
A useful form of the Strong Law of large numbers (1951) (6)
Generalization of Poincare's Formula in the Theory of Probability (1943) (6)
Seminar on Stochastic Processes, 1991 (1992) (6)
Gauge Theorem for the Neumann Problem (1986) (6)
Seminar on Stochastic Processes, 1983 (1984) (5)
Duality Under a New Setting (1984) (5)
Pao-Lu Hsu 1909-1970 (1979) (5)
Seminar on Stochastic Processes, 1989 (1990) (5)
Remarks on equilibrium potential and energy (1975) (5)
Crudely Stationary Counting Processes (1972) (5)
Probability and Doob (1998) (5)
Seminar on Stochastic Processes, 1988 (1989) (5)
HSU'S WORK IN PROBABILITY (1979) (4)
Notes on the Inhomogeneous Schrödinger Equation (1986) (4)
Some universal field equations (1972) (4)
A simple proof of DOOB's convergence theorem (1971) (4)
On recurrence of a random walk in the plane (1980) (4)
Extension of domains with finite gauge (1983) (3)
On last exit times (1960) (3)
On the renewal theorem in higher dimensions (2012) (3)
Further limit theorems (1960) (3)
On a Kind of Transformations of Matrices (1983) (3)
On a Basic Property of Markov Chains (1958) (3)
An Inequality for Boundary Value Problems (1983) (3)
Seminar on Stochastic Processes, 1982 (1983) (3)
Reminiscences of some of Paul Lévy’s ideas in Brownian Motion and in Markov Chains (1989) (3)
From Random Walks to Markov Chains (1974) (3)
Some remarks on taboo probabilities (1961) (3)
Note on a theorem on quadratic residues (1941) (3)
Probabilistic Methods in Markov Chains (1961) (3)
A New Introduction to Stochastic Processes: (In Chinese) (1997) (3)
ON THE MARTIN BOUNDARY FOR MARKOV CHAINS. (1962) (3)
The minimal solution (1960) (3)
Seminar on Stochastic Processes, 1985 (1986) (3)
The main limit theorem (1960) (2)
Central limit theorem and its ramifications (1974) (2)
The Absolute Continuity of the Distribution Functions in the Class L (1983) (2)
EQUILIBRIUM AND ENERGY (2008) (2)
Gauge Theorem for Unbounded Domains (1989) (2)
Review: L. J. Savage, The foundation of statistics (1955) (2)
On Fundamental Systems of Probabilities of a Finite Number of Events (1943) (2)
Pólya's Work in Probability (2004) (2)
ON PROJECTIVE GEOMETRY OVER FULL MATRIX RINGS (2010) (2)
BOUNDARY BEHAVIOR OF MARKOV CHAINS AND ITS CONTRIBUTIONS TO GENERAL PROCESSES (2004) (2)
The Limiting Distribution of a General Class of Statistics (1983) (2)
Reflected Brownian Motions (1983) (2)
On diverse questions of time reversing in Markov chains (and processes) (2004) (2)
On the boundary theory for Markov chains (1963) (2)
ON THE APPLICATION OF THE (2016) (2)
Probability methods in potential theory (1988) (2)
ISOMETRIES OF ORLICZ SPACES BY (2007) (1)
CONTINUOUS PARAMETER MARKOV CHAINS (2004) (1)
A Lemma on the Coefficient of Reduction of a Sum of Independent Variates (1983) (1)
Corrections to the paper “Remarks on fluctuations of sums of independent random variables” (1953) (1)
REMINISCENCES OF ONE OF DOEBLIN'S PAPERS (2004) (1)
Conditional Brownian Motion and Conditional Gauge (1995) (1)
A generalization of an inequality in the elementary theory of numbers. (1941) (1)
This paper was originally published in French as “Borel et la martingale de Saint-Pétersbourg”, in Revue d’histoire des mathématiques, 5 (1999), pp. 181–247. We thank Jean-Paul Allouche and the Société Mathématique de France for permission to publish this (2009) (1)
Corrections to My Paper "Fluctuations of Sums of Independent Random Variables" (1953) (1)
Generalized Ito Formula, Change of Time and Measure (2014) (1)
Will the Sun Rise Again (2004) (1)
A bivariate distribution in regeneration (1975) (1)
Problems for Solution: E1021-E1025 (1952) (1)
On the Power Functions of the E 2-Test and the T 2-Test (1983) (1)
On Characteristic Functions which Coincide in a Neighborhood of Zero (1983) (1)
Problems for Solution: 4210-4214 (1946) (1)
Introduction to Random Time (2003) (1)
On a Kind of Transformations of Matrix Pairs (1983) (1)
Criteria and examples (1960) (1)
On a Lemma by Kolmogoroff (1948) (1)
ON THE FUNDAMENTAL HYPOTHESES OF HUNT PROCESSES (2004) (1)
Seminar on Stochastic Processes, 1984 (1986) (1)
The Case of One Dimension (1995) (1)
The Differentiability of the Probability Transition Function of a Purely Discontinuous Stationary Markov Process on the Euclidean Space (1983) (1)
Doeblin's big limit theorem (1993) (1)
Further Results on Probabilities of a Finite Number of Events (1943) (1)
Definitions and measure-theoretic foundations (1960) (0)
GREEN'S IDEAS (1995) (0)
BIB Matrices, Simple Codes and Orthogonal Codes (1983) (0)
8 – Random walk (1974) (0)
Kai Lai Chung Interview July 25, 1994 (1994) (0)
Mean-Variance Pricing Model (2003) (0)
The moments of first entrance time distributions (1960) (0)
Collected articles from LNM : a special selection on the occasion of the memorial conference for Kai Lai Chung, Beijing 13-16 June, 2010 : the articles in this book were published between 1971 and 1985 in Lecture notes in mathematics (2010) (0)
Note on last exit decomposition (1974) (0)
“Markov chain must have a beginning” In Memory of Prof. Loo-Keng Hu (2004) (0)
1 – Distribution function (1974) (0)
Pedagogic notes on the barrier theorem (1977) (0)
Approximation of a continuous Parameter Markov Chain by Discrete Skeletons (1975) (0)
IN MEMORY OF LÉVY AND FRÉCHET (2004) (0)
Conditional Gauge and q-Green Function (1995) (0)
6 – Characteristic function (1974) (0)
Transition matrix: basic properties (1960) (0)
Classification of states (1960) (0)
2 – Measure theory (1974) (0)
Repetitive pattern and renewal process (1960) (0)
Introduction to Quantum Randomness (2003) (0)
The first infinity (1960) (0)
Generalized Ito Formula and Change of Time (1983) (0)
4 – Convergence concepts (1974) (0)
THE TROUBLE WITH BOUNDARY (1995) (0)
Mathematics in Practice: Stochastic Processes . M. Girault. Springer-Verlag, New York, 1966. 138 pp., illus. $7. (1967) (0)
A random walk example (1960) (0)
Taboo probability functions (1960) (0)
Optional random variable (1960) (0)
Problems for Solution: 4668-4672 (1956) (0)
The Ito Formula (1983) (0)
Post-exit process (1960) (0)
Review: J. L. Doob, Stochastic processes (1954) (0)
Functionals and associated random variables (1960) (0)
Quadratic Variation Process (1983) (0)
Continuity properties of sample functions (1960) (0)
Probabilistic Analysis of Semilinear Partial Differential Equations (1986) (0)
Collected articles from LNM: a special selection on the occasion of the memorial conference for Kai Lai Chung, Beijing 13-16 June, 2010 / Kai Lai Chung (2010) (0)
Review: Harald Cramér, The elements of probability theory and some of its applications (1955) (0)
Ratio limit theorems (1960) (0)
Foreword to Part 1 (2003) (0)
Poisson and Normal Distributions (1974) (0)
Local Time and Tanaka’s Formula (1983) (0)
Imbedded renewal process (1960) (0)
POSSIBILITY OF ELECTROMAGNETIC SURFACE WA VES BY PAUL (2005) (0)
Conditioning and Independence (1975) (0)
Paul Lévy’s Way to His Local Time (1991) (0)
ON THE ZEROS OF $\sum\limits^{n}_{1} \pm 1$ (2008) (0)
Foreword to Part 2 (2003) (0)
RETURN TO GREEN (1995) (0)
Extension of the Predictable Integrands (1983) (0)
Chance and Choice: Memorabilia (2004) (0)
Standard transition matrix (1960) (0)
Strong Markov property (1960) (0)
Various Related Developments (1995) (0)
SOME NOTATION AND TERMINOLOGY (2002) (0)
Simultaneous Transformation of a Hermitian Matrix and a Symmetric or Skew-Symmetric Matrix (1983) (0)
Law of large numbers. Random series (1974) (0)
Conditioning. Markov property. Martingale (1974) (0)
Advanced Problems: 6273-6275 (1979) (0)
LAST BUT NOT LEAST (1995) (0)
The two systems of differential equations (1960) (0)
Markov Processes with Infinities (2004) (0)
Remark on the conditional gauge theorem (1986) (0)
Pao-Lu Hsu 1910–1970 (1983) (0)
Almost closed and sojourn sets (1960) (0)
Kai Lai Chung Interview 1966 (1966) (0)
Stopped Feynman-Kac Functional (1995) (0)
Mean, Variance and Transforms (1974) (0)
Multinomial ratio [Paul Erdös solves a problem] (1998) (0)
The sets of constancy (1960) (0)
Solving boundary value problems by probability methods (1987) (0)
A NEW SETTING FOR POTENTIAL THEORY (Part 1) (2008) (0)
Killed Brownian Motion (1995) (0)
Problems for Solution: 4798-4803 (1958) (0)
Erratum : A new setting for potential theory (part 1) (1980) (0)
ON THE POSSIBILITY OF ELECTROMAGNETIC (2005) (0)
Book Review: M. Rosenblatt, Random processes (1962) (0)
Definition of the Stochastic Integral (2014) (0)
Kai Lai Chung Interview June 1980 (1980) (0)
Applications of the Ito Formula (1983) (0)
Probabilistic approach to boundary value problems for Schrödinger's equation (2004) (0)
Random variable. Expectation. Independence (1974) (0)
Review: B. L. van der Waerden, Mathematische Statistik (1958) (0)
Further specifications of the process (1960) (0)

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