In this paper we study random sets, with values in a separable Banach space. First we establish several useful properties of the set-valued conditional expectation and then prove some convergence ...

Abstract: Based on conditional credibility measure and conditional expected value, some properties of conditional expected value for fuzzy variables are presented, which can enrich the theoretical ...

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Abstract: This paper is concerned with the Tobit Kalman filtering for a class of discrete-time linear systems. A set of Bernoulli random variables is introduced to describe the randomly occurring ...

We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced ...

A Bayesian network (BN) is a graphical model that represents conditional independence among random variables as a directed acyclic graph (DAG). We estimate the ...

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric ...