What Does First Return Visit Mean in Random Walks?

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In the context of random walks, the term "first return visit" refers to the initial instance when the walk returns to its starting point, typically the origin, after beginning at time zero. This concept is crucial for understanding the behavior of random walks and their statistical properties. The discussion emphasizes the significance of this return time in analyzing the overall dynamics of the random walk. The first return visit is a key metric in probability theory and stochastic processes. Understanding this concept aids in deeper insights into random walk behavior.
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In random walk, what is the meaning of "fi rst return visit"
I am reading it at http://www-math.mit.edu/phase2/UJM/vol1/RMONTE-F.PDF
 
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Usual meaning: Let us assume the walk starts at the origin at time 0, then the term refers to the first time, after it starts, that it gets back to the origin.
 
mathman said:
Usual meaning: Let us assume the walk starts at the origin at time 0, then the term refers to the first time, after it starts, that it gets back to the origin.
thanks
 

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