easy · Quantitative Finance

Standard Brownian motion W_t is characterized by having increments that are independent.

What does this property imply for non-overlapping time intervals [s, t] and [u, v]?

  1. W_t and W_s must always be independent
  2. The variance of the process is constant over time
  3. The process cannot return to a previous value
  4. W_t - W_s and W_v - W_u are independent random variables

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