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I want to simulate a geometric binomial process with state/time dependent increments.

So the model is given by

\begin{align}R_t=\frac{X_t}{X_{t-1}}\end{align} \begin{align}P(R_t=u)=p(X_{t-1},t) \hspace{1cm} P(R_t = d)=1-p(X_{t-1},t)\end{align}

and \begin{align}p(X_{t-1},t)=\frac{1}{2^{|X_{t-1}|+1}}\end{align}

So e.g. how can I do this, if the initial value is equal to one? I want to use R.

The clue is, that \begin{align}P(R_t=u)=p(X_{t-1},t)\end{align} and also for $R_t=d$ is not constant?

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I can write a sketch of a MATLAB code, would it help you? –  Ilya May 21 '13 at 11:35
    
@Ilya well, to be honest, I changed the process, so for me it is not necessary anymore. I did not delete the question, since it may be relevant for user users..... –  Stat Tistician May 21 '13 at 19:40
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