Past exam of the mathematics course of the University of Cambridge / 2007 / ib / Paper 4 / 9C / ii

Table of contents
- Solution ii

Solution

Let

T_{i}^{+} = in f {n \geq 1 : X_{n} = i}

be the first positive return time. A recurrent state is one for which

P_{i} (T_{i}^{+} < \infty) = 1.

The subscript means that the Markov chain starts at

i

. The positive-time condition distinguishes a genuine return from the automatic visit at time zero.

 Ancestors (10)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version