Weak Convergence and Convergence in the Mean of Distribution Functions.
Weak convergence for empirical processes of associated sequences
Weak convergence for the row sums of a triangular array of empirical processes indexed by a manageable triangular array of functions.
Weak convergence in Hoffmann-Jorgensen sense
Weak convergence of a Dirichlet-multinomial process.
Weak* convergence of iterates of Lasota-Mackey-Tyrcha operators
Weak convergence of jump processes
Weak convergence of linear rank statistics
Weak convergence of mutually independent and under weak convergence of
For each n ≥ 1, let and be mutually independent sequences of nonnegative random variables and let each of them consist of mutually independent and identically distributed random variables with means v̅ₙ and u̅̅ₙ, respectively. Let , , t ≥ 0, and . The main result gives conditions under which the weak convergence , where X is a Lévy process, implies and , where and are mutually independent Lévy processes and .
Weak convergence of reflecting Brownian motions.
Weak convergence of summation processes in Besov spaces
We prove invariance principles for partial sum processes in Besov spaces. This functional framework allows us to give a unified treatment of the step process and the smoothed process in the same parametric scale of function spaces. Our functional central limit theorems in Besov spaces hold for i.i.d. sequences and also for a large class of weakly dependent sequences.
Weak convergence of the corrected empirical -statistics under mixing condition. (Convergence faible de la -statistique empirique corrigée en condition de mélange.)
Weak convergence to fractional Brownian motion in some anisotropic Besov space
We give some limit theorems for the occupation times of 1-dimensional Brownian motion in some anisotropic Besov space. Our results generalize those obtained by Csaki et al. [4] in continuous functions space.
Weak convergence to Ocone martingales: a remark.
Weak convergence to the law of the brownian sheet
Weak Hölder convergence of processes with application to the perturbed empirical process
We consider stochastic processes as random elements in some spaces of Hölder functions vanishing at infinity. The corresponding scale of spaces is shown to be isomorphic to some scale of Banach sequence spaces. This enables us to obtain some tightness criterion in these spaces. As an application, we prove the weak Hölder convergence of the convolution-smoothed empirical process of an i.i.d. sample under a natural assumption about the regularity of the marginal distribution function F of the...
Weak inequalities for exit times and analytic functions
Weak infinitesimal generator for a stochastic partial differential equation with time delay.
Weak infinitesimal operators and stochastic differential games.
This article considers the problem of finding the optimal strategies in stochastic differential games with two players, using the weak infinitesimal operator of process xi the solution of d(xi) = f(xi,t,u1,u2)dt + sigma(xi,t,u1,u2)dW. For two-person zero-sum stochastic games we formulate the minimax solution; analogously, we perform the solution for coordination and non-cooperative stochastic differential games.
Weak law of large numbers for i.i.d. fuzzy random variables
In this paper, weak laws of large numbers for sum of independent and identically distributed fuzzy random variables are obtained.