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A martingale can be constructed from a random walk. Can someone give a numerical example of how this can be done together with some little proof to spice up the example?

Thanks in anticipation

Christian Prince
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    I'm not sure I understand what you want to get here. A symmetric random walk is already a martingale. Do you want to know how to construct a martingale from an asymmetric random walk? (One way to do it is to subtract off the effective drift: if a walk goes to the right with probability $0.5+\delta$, then its effective drift is $2\delta$ per time step. Thus if $X_n$ is a random walk which goes to the right with probability $0.5+\delta$, then $X_n-2\delta n$ is a martingale.) – Ian Aug 23 '15 at 23:22
  • Thanks @Ian for this contribution – Christian Prince Aug 23 '15 at 23:36

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