Brownian Motion

Definition

A process $(B_t)_{t\ge 0}$ is Brownian motion if:

1. $B_0=0$
2. It has independent increments
3. For every $s

$$ B_t-B_s\sim N(0,t-s) $$

4. Its sample paths are continuous almost surely

Interpretation

Brownian motion is the canonical model of continuous-time random motion with Gaussian increments and continuous paths.

Source Links

• STA447
• Phase 6 Atomic Reading Order
• Phase 6 — Brownian Motion 基础
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