Random Walks and Brownian Motion Lecture 2
نویسنده
چکیده
The following lecture will consider mainly the simple random walk in 1-dimension. The SRW will satisfy us for now as it can be generalized with a few simple assumptions to various other random walks. Our main topics are the Wald identities along with the derivation of the moment generating function of the first passage time for 1-dimensional SRW and the SRW properties such as: the arcsine laws for the last zero and fraction of time above axis, time reversal and equidistribution of positive time for SRW bridge. We will see that there are several properties whose probability distribution is similar asymptotically to the arcsine function.
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تاریخ انتشار 2011