nLab Brownian motion

Brownian motion is an example of a stochastic process. Brownian motion B tB_t is a stochastic process on [0,)[0,\infty) with the following properties:

  • B 0=0B_0=0 almost surely.

  • The increments B tB sB_t-B_s are independent and normally distributed N(0,ts)N(0,t-s) for t>st \gt s.

  • The function tB tt\mapsto B_t is continuous.


For now see

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