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by macro-b
1908 days ago
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A dynamic system is a system whose evolution doesn’t simply depend on its input at time t, but also to its internal state. In this case the wealth at time t does not simply depend on the outcome of the coin toss, you also need to know the value of the wealth before the coin toss. |
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1. A state space X
2. An evolution map f: X -> X
3. A measure \mu on X, preserved by f (such that f_*\mu = \mu) and where \mu(X) = 1.
To represent a series of i.i.d. random variables you can typically just represent them as a sequence of values with a joint probability distribution as the invariant measure.
If you've got a space X of such sequence you can also add the current value to it to get IR x X, with a map f: (x,t) -> x * 1.5 if t[0] is heads & x * 0.6 otherwise. But you'll have to tell me it's invariant measure because I can't come up with one.