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I am doing a self-study of stochastic processes using
Hoel, Port, and Stone's "Introduction to Stochastic
Processes".
I am having trouble coming up with a formal solution
to problem 13 of chapter 1. Here is the statement
of the problem:
Let X_n be a Markov chain whose state space is a subset
of {0,1,2,...} and whose transition function P is such
that:
\Sigma_y yP(x,y) = Ax + B, for some constants A and B.
Show that E[X_{n+1}] = A*E[X_n] + B, (where E[] denotes
the expected value.)
Can anyone offer any advicee on how to start this
problem?
--Andrew
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<pre wrap="">I am doing a self-study of stochastic processes using
Hoel, Port, and Stone's "Introduction to Stochastic
Processes".
I am having trouble coming up with a formal solution
to problem 13 of chapter 1. Here is the statement
of the problem:
Let X_n be a Markov chain whose state space is a subset
of {0,1,2,...} and whose transition function P is such
that:
\Sigma_y yP(x,y) = Ax + B, for some constants A and B.
Show that E[X_{n+1}] = A*E[X_n] + B, (where E[] denotes
the expected value.)
Can anyone offer any advicee on how to start this
problem?
--Andrew
</pre>
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</body>
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