In 1965, Njastad [2] introduced the notion of α-sets in topological space. In 1983, Mashhour et al. [1] introduced, with the help of α-sets, a weak form of continuity which they termed as α-continuity. Noiri [3] introduced the same concept, but under the name strong semicontinuity. Noiri [4] defined with the aid of α-sets a new weakened form of continuous mapping called weakly α-continuous mapp...

ASYMPTOTICS AND CONFIDENCE ESTIMATION IN SEGMENTED REGRESSION MODELS Rebekah Ann Robinson May 11, 2012 Standard regularity assumptions for regression models are not satisfied in segmented regression models with an unknown change point, and consequently standard asymptotic results and inferential methods for confidence estimation are not applicable. This dissertation considers a clustered segmen...

Given a pair of convex conjugate functions f and f∗, we investigate the relationship between local Lipschitz continuity of ∇f and local strong convexity properties of f∗.

Strong convergence results on tamed Euler schemes, which approximate stochastic differential equations with superlinearly growing drift coefficients that are locally one-sided Lipschitz continuous, are presented in this article. The diffusion coefficients are assumed to be locally Lipschitz continuous and have at most linear growth. Furthermore, the classical rate of convergence, i.e. one–half,...

Brownian motions in the innnite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent one-dimensional Brownian motions. The proof involves continuous tensor products and continuous quantum measurements. A by-product: a Brownian motion in a separab...

We extend the taming techniques for explicit Euler approximations of stochastic differential equations (SDEs) driven by Lévy noise with super-linearly growing drift coefficients. Strong convergence results are presented for the case of locally Lipschitz coefficients. Moreover, rate of convergence results are obtained in agreement with classical literature when the local Lipschitz continuity ass...

BACKGROUND One major goal of the Patient-Centered Medical Home (PCMH) is to improve continuity of care between patients and providers and reduce the utilization of non-primary care services like the emergency department (ED). OBJECTIVE To characterize continuity under the Veterans Health Administration's PCMH model--the Patient Aligned Care Team (PACT), at one large Veterans Affair's (VA's) p...

A member of a class of evolution systems is defined by averaBing a oneparameter family of invertible transformations G with a semigroup T The resulting evolution system, U(t,s) G(t)T(t-s)G(s) -1, preserves continuity and strong continuity, and in case G is a linear family, may have an identifiable generator and resolvent both of which are constructed from T. Occurrences of the class of evolutio...

This paper studies the approximation of optimal control policies by quantized (discretized) policies for a very general class of Markov decision processes (MDPs). The problem is motivated by applications in networked control systems, computational methods for MDPs, and learning algorithms for MDPs. We consider the finite-action approximation of stationary policies for a discrete-time Markov dec...

Many theoretical results in the machine learning domain stand only for functions that are Lipschitz continuous. Lipschitz continuity is a strong form of continuity that linearly bounds the variations of a function. In this paper, we derive tight Lipschitz constants for two families of metrics: Mahalanobis distances and bounded-space bilinear forms. To our knowledge , this is the first time the ...