“Brownian motion”的概念、定义、习题解题方法及翻译-数学辞典

单词

Brownian motion

释义

Brownian motion

Brownian motion, named after the Scottish botanist Robert Brown (1773–1858), describes the random motions of a particle in a medium. Within mathematics, the term relates to a stochastic process introduced by Norbert Wiener. The Wiener process Wt for t≥0, models the movement of such a particle beginning at the origin at t = 0 and is characterized by the following properties:

(i) W0 = 0

(ii) Future displacements Wt + u – Wt (where u ≥ 0) are independent of Ws where s ≤ t.

(iii) Wt + u – Wt (where u ≥ 0) has normal distribution with mean 0 and variance u.

(iv) Wt is continuous in t.

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