We propose an approximation of expectation ({\it pseudo
expectation}) of Markov process, which is originally discussed by 
Watanabe and Sawai in the context of randomized decoding algorithm for LDPC.
We show a bound of the difference between pseudo expectation and expectation, 
and give a deviation probability with respect to the the pseudo expectation.
As an example, we study certain kind of urn model, which is a simplified model 
of Watanabe and Sawai algorithm, and apply our results to the model.