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I have a test tomorrow about Stochastics Process and I couldn't solve the following questions:

A gambler starts with 500\$ and plays till he runs out of money. In each round the probability to win 100\$ is 0.2, the probability to win 1000\$ is 0.05 and the probability to lose 100\$ is 0.75. The time between two rounds is distributed exponentially with \begin{equation} \lambda = 0.2 \end{equation} and if the gambler has 1000*n\$ where n is integer the time to the next round is distributed exponentially with \begin{equation} \lambda = 0.1 \end{equation}

a) Describe the gambler's profit as a continuous-time Markov Chain.

b) Find the infinitsimal generator.

c) Find an equivalent unfirom continous-time Markov Chain.


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What have you tried? We won't just answer your homework. We might give hints, or tell you were you went awry, though. – vonbrand Feb 2 '13 at 20:15
Ok, Sorry for not describing this earlier, but I tried to look at this as a uniform chain with lambda = 0.2 and in order to avoid the cases in which lambda = 0.1, I add a probabilty for earning 0\$ when the amount of money is 1000*N\$ for an integer N. This chain is equivalent to the one described in the question. Now all we need is to find the subordinated chain, but this is where I stuck, because there are too many options to get from the state i to the state j. I tried to think about other directions, without succeed. – Guy Feb 2 '13 at 21:18

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