Brownian Motion

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Last updated 4:12 PM on 5/10/26
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4 Terms

1
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What is a stochastic process?

A collection of random variables indexed by time

2
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What is a sample path?

An outcome of the stochastic process from a particular sample point

3
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What is an adapted process for a stochastic process?

X is adapted to the filtration so at time t, the value of the process only depends on information available up to time t

4
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What are two important properties of normally distributed random variables?

Any linear combination of independent Gaussian random variables is Gaussian, and if (X,Y) is Gaussian, then covariance is zero