A Study On The Simple Random Walk


An important class of Markov chain problems is the random walk problems. In a random walk the state of the Markov chain are the integers and the jumps of the chain from state are only to neighbor states . There are many variations on this basic design. When the state space of the chain is finite it is sometimes called the gamblers ruin problem. There are various martingale and Markov chain methods to analyze probabilistic characteristics of a simple random walk. In this study a simple random walk is defined and the first time that this random walk visits the state is analyzed by using generating functions. is calculated in terms of the probabilities and .


Markov chain; random walk; generating functions.

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