Approximation of random functions by stochastic Bernstein polynomials in capacity spaces

Given a submodular capacity space, we firstly obtain a quantitative estimate for the uniform convergence in the Choquet p-mean, 1\le p<\infty, of the multivariate stochastic Bernstein polynomials associated to a random function. Also, quantitative estimates concerning the uniform convergence in capacity in the univariate case are given.

p,q-Growth of Meromorphic Functions and the Newton-Padé Approximant

In this paper, we have considered the generalized growth (p,q-order and p,q-type) in terms of coefficient of the development pnn given in the (n, n)-th Newton-Padé approximant of meromorphic function. We use these results to study the relationship between the degree of convergence in capacity of interpolating functions and information on the degree of convergence of best rational approximation on a compact of ℂ (in the supremum norm). We will also show that the order of meromorphic functions puts an upper bound on the degree of convergence.

Averaging principle for SDEs of neutral type driven by G-Brownian motion

In this paper, we investigate the averaging principle for SDEs of neutral type driven by [Formula: see text]-Brownian motion. The solutions of convergence in the sense of [Formula: see text]th moment and convergence in capacity between standard form and the corresponding averaged form are considered. Two examples are presented to demonstrate the applications of the averaging principle.

On the rapidly convergence in capacity of the sequence of holomorphic functions

In this paper, we are interested in finding sufficient conditions on a Borel set X lying either inside a bounded domain D ? Cn or in the boundary ?D so that if {rm}m?1 is a sequence of rational functions and {fm}m?1 is a sequence of bounded holomorphic functions on D with {fm-rm}m?1 is convergent fast enough to 0 in some sense on X then the convergence occurs on the whole domain D. The main result is strongly inspired by Theorem 3.6 in [3] whether the f fmg is a constant sequence.

Convergence in capacity of plurisubharmonic functions with given boundary values

In this paper, we study the convergence in the capacity of sequence of plurisubharmonic functions. As an application, we prove stability results for solutions of the complex Monge–Ampère equations.

Convergence in capacity of rational approximants of meromorphic functions

Let f be meromorphic on the compact set E ? C with maximal Green domain of meromorphy Ep(f), p(f) < ?. We investigate rational approximants with numerator degree ? n and denominator degree ? mn for f. We show that the geometric convergence rate on E implies convergence in capacity outside E if mn = o(n) as n ? 1. Further, we show that the condition is sharp and that the convergence in capacity is uniform for a subsequence ? ? N.

Convergence in Capacity

In this note we study the convergence of sequences of Monge–Ampère measures ﹛(ddcus)n﹜, where ﹛us﹜ is a given sequence of plurisubharmonic functions, converging in capacity.