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Can someone point me towards a resource that will help me analyse a 1-d random walk where each step can take 1 of say 6 values with known probabilities. Not a continuous time random walk, time intervals are discrete and equal.

Patrick
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  • Pen & Paper. $ $ $ $ – Newb Dec 27 '13 at 04:28
  • Are you sure. For a simple symmetric random walk the expected value is zero (-1, +1 with each probability of 0.5). – Patrick Dec 27 '13 at 07:22
  • Are you sure. For a simple symmetric random walk the expected value is zero (-1, +1 with each probability of 0.5). The randomness of the walk and the size of the step are assumed to be independent" - not sure what this means. Each size of the step has a probability which is fixed and therefore independent of every other aspect of the walk. However the walk certainly is not independent of the step size. – Patrick Dec 27 '13 at 07:40

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You can replace the step length by its expected value (a constant).

The randomness of the walk and the size of the step are assumed to be independent.

user44197
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  • Are you sure. For a simple symmetric random walk the expected value is zero (-1, +1 with each probability of 0.5). – Patrick Dec 27 '13 at 07:34
  • Are you sure. For a simple symmetric random walk the expected value is zero (-1, +1 with each probability of 0.5). The randomness of the walk and the size of the step are assumed to be independent" - not sure what this means. Each size of the step has a probability which is fixed and therefore independent of every other aspect of the walk. However the walk certainly is not independent of the step size. – Patrick Dec 27 '13 at 07:42