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Hello, so a classic example of the stochastic process that is both discrete in state -space and discrete in time is the markov chain.
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Consider a simple weather model where the state -space consists of just two states, rainy and sunny.
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The system transitions between these two states at discrete time intervals, days.
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The process is stochastic because the transition from one state to another is probabilistic, not deterministic.
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This process fits into the category of discrete state space and discrete time for the following reasons.
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1.
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Discrete state space.
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There are a limited number of states, rainy, sunny, and these states are distinct and countable.
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2.
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Discrete time.
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The transitions between states occur at fixed, discrete intervals, which is daily.
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Now, regarding the determination of the steady -state probability vector, w, for an ergodic markov chain with a given transition probability, matrix p, the steps are as follows...