Random Walk and the Theory of Brownian Motion
E92913
"Random Walk and the Theory of Brownian Motion" is a mathematical work by Mark Kac that rigorously develops the connection between discrete random walks and continuous Brownian motion within probability theory.
Observed surface forms (1)
| Surface form | Occurrences |
|---|---|
| Mark Kac | 0 |
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical work ⓘ mathematician ⓘ monograph ⓘ |
| aim | to present a rigorous development of Brownian motion from random walks ⓘ |
| audience |
advanced students of probability
ⓘ
mathematical physicists ⓘ researchers in probability theory ⓘ |
| author | Mark Kac ⓘ |
| contribution |
clarified probabilistic interpretation of Brownian motion
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influenced later work on stochastic calculus ⓘ provided rigorous link between discrete random walks and continuous Brownian motion ⓘ |
| field |
probability theory
ⓘ
probability theory ⓘ stochastic processes ⓘ |
| focusesOn |
connection between random walks and Brownian motion
ⓘ
probabilistic foundations of diffusion ⓘ rigorous derivation of Brownian motion as a scaling limit ⓘ |
| genre |
mathematics literature
ⓘ
scientific literature ⓘ |
| hasAuthor | Mark Kac ⓘ |
| language | English ⓘ |
| mainTopic |
Brownian motion
ⓘ
continuous-time stochastic processes ⓘ discrete-time stochastic processes ⓘ limit theorems ⓘ random walk ⓘ |
| relatedTo |
heat equation
ⓘ
mathematical physics ⓘ statistical mechanics ⓘ theory of diffusion ⓘ |
| subjectArea |
Brownian motion in physics
ⓘ
mathematical modeling of physical phenomena ⓘ random processes ⓘ |
| usesConcept |
Gaussian distributions
ⓘ
Markov processes ⓘ
surface form:
Markov property
Brownian motion ⓘ
surface form:
Wiener process
central limit theorem ⓘ convergence in distribution ⓘ independent increments ⓘ probability measures ⓘ random variables ⓘ scaling limits ⓘ transition probabilities ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.