We study the problem of statistical inference of continuous-time diffusion processes, and develop methods for modeling threshold diffusion processes in particular. We derive the limiting properties of the quasi-likelihood estimator. We also propose a quasi-likelihood ratio test statistic for testing threshold diffusion process against linear alternative. We begin in Chapter 1 with an introducti...

We compare the asymptotic local power of upper-tail unit root tests against an explosive alternative based on ordinary least squares (OLS) and quasi-di erenced (QD) demeaning/detrending. We nd that under an asymptotically negligible initialization, the QD-based tests are near asymptotically e cient and generally o er superior power to OLS-based approaches; however, the power gains are much more...

The local stability of a quasi-linear age-size structured population model studied in Tchuenche (2007) is analysed. If a certain threshold parameter known as the basic reproductive rate is less than unity, then the trivial steady state is locally asymptotically stable. Also, it is shown that if the only real root of the equation R(m′) = 1 is negative, then, the non trivial steady state is local...

We construct random iterative processes for weakly contractive and asymptotically nonexpansive random operators and study necessary conditions for the convergence of these processes. It is shown that they converge to the random fixed points of these operators in the setting of Banach spaces. We also proved that an implicit random iterative process converges to the common random fixed point of a...

Abstract In this paper, we propose a modified proximal point algorithm based on the Thakur iteration process to approximate common element of set solutions convex minimization problems and fixed points two nearly asymptotically quasi-nonexpansive mappings in framework $\operatorname{CAT}(0)$ CAT ( <mml:m...

In this paper, we define and study convergence of an Ishikawa type iteration scheme with a new and weaker control condition for two nonself asymptotically quasi-nonexpansive mappings on a uniformly convex Banach space.

The purpose of this paper is to introduce a modified Halpern-type iteration algorithm and prove strong convergence of the algorithm for quasi-φ-asymptotically non-expansive mappings. Our results improve and extend the corresponding results announced by many others.