A New Probability Measure-Valued Stochastic Process with Ferguson-Dirichlet Process as Reversible Measure

A new probability measure-valued stochastic process with Ferguson-Dirichlet process as reversible measure∗

A new diffusion process taking values in the space of all probability measures over [0,1] is constructed through Dirichlet form theory in this paper. This process is reversible with respect to the Ferguson-Dirichlet process (also called Poisson Dirichlet process), which is the reversible measure of the Fleming-Viot process with parent independent mutation. The intrinsic distance of this process...

The Entrance Space of a Measure - Valued Markov Branching Process

We explicitly identify the possible probability entrance laws for a class of measure-valued processes that are constructed by taking a particular measure-valued Markov branching process and conditioning it to stay away from the zero measure trap. The set of extreme points of the entrance space is larger than the state space of the conditioned process, and contains elements which correspond to "...

Hyperreal-Valued Probability Measures Approximating a Real-Valued Measure

A New Fuzzy-Valued Additive Measure

In this paper, we firstly invoke gradual Hausdorff metric to define a new additive fuzzy-valued measure on the ordinary measurable space. Then, from the view of a fuzzy number as a crisp interval of gradual numbers, we show that the new fuzzy-valued measure can be characterized by two gradual number-valued measures. Finally, we investigate some of its properties and structural characterizations.

Time-changed Extremal Process as a Random Sup Measure

A functional limit theorem for the partial maxima of a long memory stable sequence produces a limiting process that can be described as a β-power time change in the classical Fréchet extremal process, for β in a subinterval of the unit interval. Any such power time change in the extremal process for 0 < β < 1 produces a process with stationary max-increments. This deceptively simple time change...