Branching random walk: Difference between revisions
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In probability theory, a branching random walk is a stochastic process whose value at any point in discrete time is a set of point in some space, such as the real line, such that each point may have one or more descendants at the next point in time, located at places resulting from addition of a random variable to the location of their parents.
For example, for a binary branching random walk, suppose X0 = 0, and X1,1 and X1,2 are the two children of X0, and are indenpendent N(0, 1) random variables. Then at time 2, X2,1 and X2,2 would be the sum of X1,1 and a N(0, 1) random variable, and X2,1 and X2,1 would be the sum of X1,2 and a N(0, 1) random variable, and so on.