Weak Convergence of Generalized Empirical Processes Relative to $d_q$ Under Strong Mixing

Convergence to Lévy Stable Processes under Strong Mixing Conditions

For a strictly stationary sequence of random vectors in R we study convergence of partial sums processes to Lévy stable process in the Skorohod space with J1-topology. We identify necessary and sufficient conditions for such convergence and provide sufficient conditions when the stationary sequence is strongly mixing.

Weak and strong convergence theorems for a finite family of generalized asymptotically quasinonexpansive nonself-mappings

In this paper, we introduce and study a new iterative scheme toapproximate a common xed point for a nite family of generalized asymptoticallyquasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weakconvergence theorems of the proposed iteration are established. The main resultsobtained in this paper generalize and rene some known results in the currentliterature.

@bullet , @bullet Weak Convergence of Multidimensional Empirical Processes for Stationary ¢-mixing Processes

Weak Convergence of Stationary Empirical Processes

We offer an umbrella type result which extends the convergence of classical empirical process on the line to more general processes indexed by functions of bounded variation. This extension is not contingent on the type of dependence of the underlying sequence of random variables. As a consequence we establish the weak convergence for stationary empirical processes indexed by general classes of...

Empirical Processes: General Weak Convergence Theory

The lack of measurability of the empirical process with respect to the sigma-field generated by the ‘natural’ l∞ metric, as illustrated in the previous notes, needs an extension of the standard weak convergence theory that can handle situations where the converging stochastic processes may no longer be measurable (though the limit will be a tight Borel measurable random element). Of course, an ...