# J. L. Doob: Foundations of stochastic processes and probabilistic potential theory

@article{Getoor2009JLD, title={J. L. Doob: Foundations of stochastic processes and probabilistic potential theory}, author={Ronald Getoor}, journal={Annals of Probability}, year={2009}, volume={37}, pages={1647-1663} }

During the three decades from 1930 to 1960 J. L. Doob was, with the possible exception of Kolmogorov, the man most responsible for the transformation of the study of probability to a mathematical discipline. His accomplishments were recognized by both probabilists and other mathematicians in that he is the only person ever elected to serve as president of both the IMS and the AMS. This article is an attempt to discuss his contributions to two areas in which his work was seminal, namely, the…

## 6 Citations

### Notes on stochastic processes Paul Keeler

- Mathematics
- 2018

A stochastic process is a type of mathematical object studied in mathematics, particularly in probability theory, which can be used to represent some type of random evolution or change of a system.…

### Notes on stochastic processes

- Mathematics
- 2016

A stochastic process is a type of mathematical object studied in mathematics, particularly in probability theory, which shows some type of a randomness. There are many types of stochastic processes…

### How to Base Probability Theory on Perfect-Information Games

- EconomicsBull. EATCS
- 2010

The standard way of making probability mathematical begins with measure theory, but an alternative that begins with game theory is reviewed, and how this approach differs from the measure-theoretic approach is discussed.

### Doob's ω-transform of parabolic problem for fractional Laplacian

- MathematicsApplicable Analysis
- 2021

This paper studies the existence of nonnegative solutions for the following parabolic problem {Lωu+∂u∂t=0,inRd×(0,T),u(x,0)=u0(x),inRd, where T>0, Lω is a selfadjoint operator associated with a reg...

### The concept of velocity in the history of Brownian motion

- PhysicsThe European Physical Journal H
- 2020

Interest in Brownian motion was shared by different communities: this phenomenon was first observed by the botanist Robert Brown in 1827, then theorised by physicists in the 1900s, and eventually…

## References

SHOWING 1-10 OF 10 REFERENCES

### Doob: a half-century on

- Psychology
- 2005

Probability theory, and its dynamic aspect stochastic process theory, is both a venerable subject in that its roots go back to the midseventeenth century, and a young one in that its modern…

### A Conversation with Joe Doob

- Education
- 1997

Joseph L. Doob was born in Cincinnati, Ohio, February 27, 1910. He received the degrees A.B. in 1930, A.M. in 1931 and Ph.D. in 1932 from Harvard University. From 1932 to 1934 Doob did postdoctoral…

### Two . dimensional Brownian Motion and Harmonic Functions

- Mathematics

1. The purpose of this paper is to investigate the properties of two-dimensional Brownian motions’ and to apply the results thus obtained to the theory of harmonic functions in the Gaussian plane.…

### Joseph Leo Doob, 1910-2004

- Engineering
- 2011

D. Burkholder and P. Protter. Joseph Leo Doob, 1910–2004. Stochastic Process. Appl., 115(7):1061–1072, 2005. Reprinted with permission of Elsevier Inc. An electronic version is available at…

### SOME THEOREMS CONCERNING BROWNIAN MOTION

- Mathematics
- 1956

Given a random time T and a Markoff process X(t) with stationary transition probabilities, one can define a new process X'(t) =X(t + T). It is plausible, if T depends only on the X(t) for r less than…

### Strong Markov Processes

- Mathematics
- 1977

Suppose that {xt} is a Markov process. If it is known that \(x_{t_0 } \), the process can be thought of as “beginning afresh” thereafter as though x had been its initial state.

### La théorie générale des processus de Markov à temps continu

- 1968

### La théorie générale des processus de MarkovMarkovà temps continu

- La théorie générale des processus de MarkovMarkovà temps continu
- 1968