Question

what is brownin motion with one example no wrong answers

Answer 1

for a fixed ϵ >0, I want to show that almost surely (ie with probability 1), a standard brownian motion Wt would change sign over [o,ϵ ]. I thought about defining a random variable Ut=sign(Wt) which would satisfy : (1+Ut)/2 follows symmetric Bernoulli distribution But I can't conclude with this.

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Answer 2

Brownian motion (named after the Scottish botanist Robert Brown) or pedesis is the seemingly random movement of particles suspended in a fluid (i.e. a liquid such as water or air) or the mathematical model used to describe such random movements, often called a particle theory.
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