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This paper presents asymptotic formulas in the case of the following two problems for the Pucci's extremal operators M ± . It is considered the solution u ε (x) of − ε 2 M ± ∇ 2 u ε + u ε = 0 in Ω such that u ε = 1 on Γ. Here, Ω ⊂ R N is a domain (not necessarily bounded) and Γ is its boundary. It is also considered v (x , t) the solution of v t − M ± ∇ 2 v = 0 in Ω × (0 , ∞) , v = 1 on Γ × (0 , ∞) and v = 0 on Ω × { 0 }. In the spirit of their previous works [Berti D, Magnanini R. Asymptotics for the resolvent equation associated to the game-theoretic p-laplacian. Appl Anal. 2019;98(10):1827–1842.; Berti D, Magnanini R. Short-time behavior for game-theoretic p-caloric functions. J Math Pures Appl (9). 2019;(126):249–272.], the authors establish the profiles as ϵ or t → 0 + of the values of u ε (x) and v (x , t) as well as of those of their q-means on balls touching Γ. The results represent a further step in the extensions of those obtained by Varadhan and by Magnanini-Sakaguchi in the linear regime. [ABSTRACT FROM AUTHOR]

This article reexamines the scope of a two-stage methodology for constructing a fixed-width confidence interval for the difference between two independent normal population means. We address directly the problem in a Behrens-Fisher situation, that is, when the variances of the two populations are both unknown and unequal. However, we show that the proposed methodology remains valid when the two variances are equal but unknown. We apply a two-stage procedure to the Behrens-Fisher situation using two approaches. In the first approach, we work with the differences of each observation in the first sample with all observations in the second sample. In the second approach, we work with the differences of paired observations from samples 1 and 2. Next, to overcome the problem of oversampling associated with the two-stage procedures, we apply the bootstrap methodology to modify the two-stage procedures. These methods, with and without bootstrapping, are compared with the help of a large-scale simulation study. [ABSTRACT FROM AUTHOR]

This work is devoted to the dynamical system (SRB): d (∂̸ h ( x ( t )))/ dt +∇ Φ ( x ( t ))∋ 0, with h a proper lower semicontinuous convex function. Existence and uniqueness of solutions are examined. Systems (SRB) include the class of gradient systems with respect to a Hessian Riemannian metric induced by a convex Legendre function h : . Moreover, class (SRB) is closed in a variational sense: links are made with regularized Lotka-Volterra systems and the limit equations obtained by letting the barrier parameter go to 0. Of particular interest is the case h ( x )= (1/2)| x | 2 +δ C ( x ): this way, one obtains a new gradient-projection method. System (SRB) bears a direct relation with the minimization of Φ over the domain of ∂̸ h ; the asymptotic behaviour of solutions, as time goes to infinity, is a real issue, which is addressed for a convex Φ and a h of the form h = k +δ C , with k convex and C a finite-dimensional polyhedron. [ABSTRACT FROM AUTHOR]