A random walk construction of Brownian motion with drift
نویسنده
چکیده
Brownian motion with drift is constructed on the real line as the almost sure limit of a sequence of random walks. Central to the construction is an embedded varying environment branching process, which encodes the sample path behaviour of the limiting diiusion. We show how a single small time bound on the normed limit of the branching process leads to diierent small and large time bounds on the expected position of the process. This method of construction has previously been used to construct diiusion on frac-tals. Here the method is extended to the use of a varying rather than xed environment branching process.
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