Question
Problem: Suppose you have a recurrent chain in continuous time with transition rate Q(0,j)from state 0 to state j > 0. Starting in state 0,
Problem: Suppose you have a recurrent chain in continuous time with transition rate Q(0,j)from state 0 to state j > 0. Starting in state 0, let H(0,j) be the total time spent in state 0 before the first jump from 0 to j.
a) What is the distribution of H(0,j)?
b) What is the joint distribution of H(0,j) and H(0, k) for different j and k ?
In each case,explain as best you can.
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Introduction to Real Analysis
Authors: Robert G. Bartle, Donald R. Sherbert
4th edition
471433314, 978-1118135853, 1118135857, 978-1118135860, 1118135865, 978-0471433316
