The standard Brownian motion
Consider a person walking in the integers according to the following rule: start at time n = 0 at s(0) = 0, ±1, ± 2 , . . . and flip a true coin; if tails comes up, step at time n = 1 to s(1) = s(0) - 1; if heads comes up, step to s(l) = s(0) + l. Coming, thus, at time n - 1 to s(n - 1), flip the coin; if tails comes up, step at time n to s(n) = s(n - 1) - 1, if heads comes up, step to s(n)= s(n - 1) + 4; etc.
KeywordsBRowNian Motion Passage Time Sample Path Lower Class Iterate Logarithm
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