Abstract
This paper is devoted to studying what call irregular random walk on the non-negative integers. The random walk plays an essential role in different areas of applications. It models many problems in a way to make it easier to handle and study. A random walk, in general, is a sequence of partial sums of independent identically distributed random variables. The type which well be considered in is partial sums of random variables that are not necessarily independent or identically distributed. The type of random walk of being transient or recurrent is one of the most important concepts to be studied. The random walk is said to be recurrent if the walker starts at some state and the return time to the starting state is finite almost surely, and transient if there is a positive probability of not returning to the starting state. The recurrent random walk is positive if the mean return time is also finite, and it is null recurrent otherwise.
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