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In this article, we discuss a linear regression change-point model with skew normal errors. We propose a testing procedure, based on a modified version of the Schwarz information criterion, which is named the modified information criterion (MIC) to locate change points in such a linear regression model. Due to the difficulty of derivation of the asymptotic null distribution of the associated test statistic analytically, the empirical critical values at different significance levels are approximated through simulations. Simulations have also been conducted under different changes among parameters of interest with various sample sizes to investigate the performance of the proposed test. Such a procedure has been applied on a NASA data to illustrate the detecting process.

This paper is devoted to establish an existence and uniqueness result of one-dimensional reflected backward stochastic differential equations with time-delayed generators (RBSDEs with time-delayed generators, in short). Our proof is based on approximation via a penalization method.

This paper deals with the homogenization problem of one-dimensional pseudo-elliptic equations with a rapidly varying random potential. The main purpose is to characterize the homogenization error (random fluctuations), i.e., the difference between the random solution and the homogenized solution, which strongly depends on the autocovariance property of the underlying random potential. It is well known that when the random potential has short-range dependence, the rescaled homogenization error converges in distribution to a stochastic integral with respect to standard Brownian motion. Here, we are interested in potentials with long-range dependence and we prove convergence to stochastic integrals with respect to the Hermite process.

Cyclic mappings have appeared prominently in fixed point theory during the last decade. They have also their applications in global optimization problems. Note that p -cyclic mappings are extensions of cyclic mappings over p number of sets. In this paper we introduce two p -cyclic contractions in probabilistic spaces. We have two corresponding fixed point theorems using third-order Hadzic-type t -norm and minimum t -norm, respectively. One of the probabilistic contractions is of Ciric type while the other is a general contraction. One illustrative example is given. The space we consider here is a 2-Menger space which is an extension of a probabilistic metric space in the same vein as the 2-metric spaces are extensions of metric spaces.

In this paper, we present some results concerning the existence and the stability of solutions for some functional integral equations of Riemann–Liouville fractional order with random effects and multiple delay, by applying a random fixed point theorem with stochastic domain and the measure of noncompactness.