Consider a stochastic process with two probability laws, one of which is absolutely continuous with respect to the other. Under each law, we look at a process consisting of the conditional distributions of the future given the past. Blackwell and Dubins (1962) showed in discrete case that those...

In this note, we give an example to show that the prediction process may lost Markov property if the future of the process which generates the known past is not included in the future to be predicted.

We study convergence in law of measurable processes with a general state space and a parameter set. The space of measurable functions are first investigated and we examine properties of probability measure on the space. A necessary and sufficient condition for convergence in law of measurable...

For the class of distortion risk measures, a natural estimator has the form of L-statistics. In this article, we investigate the large sample properties of general L-statistics based on weakly dependent data and apply them to our estimator. Under certain regularity conditions, which are somewhat...