Suppose that a Wiener process gains a known drift rate at some unobservable disorder time with some zero-modified exponential distribution. The process is observed only at known fixed discrete time epochs, which may not always be spaced in equal distances. The problem is to detect the disorder time as quickly as possible by an alarm which depends only on the observations of Wiener process at th...

Aquatic macroinvertebrates, which play a significant role in the food chain of an ecosystem, are used in fresh water quality assessment to identify the environmental stress resulting from a variety of anthropogenic disturbances. Seasonal surveys of macroinvertebrate communities were conducted from April 2013 to March 2014 in Chhariganga oxbow lake of Nadia District of West Bengal, an eastern st...

The aim of the paper is to provide some regularity results for stochastic convolutions corresponding to stochastic Volterra equations in separable Hilbert space. We study convolutions of the form WΨ(t) := ∫ t 0 S(t − τ)Ψ(τ)dW (τ), t ≥ 0, where S(t), t ≥ 0, is so-called resolvent for Volterra equation considered,Ψ is an appropriate process and W is a cylindrical Wiener process. In the paper we e...

Wiener process with instantaneous reflection in narrow tubes of width ε ≪ 1 around axis x is considered in this paper. The tube is assumed to be (asymptotically) non-smooth in the following sense. Let V (x) be the volume of the cross-section of the tube. We assume that 1 ε V (x) converges in an appropriate sense to a non-smooth function as ε ↓ 0. This limiting function can be composed by smooth...

Abstract: This paper deals with the design of Optimal Step-Stress Partially Accelerated Degradation Test (PADT) using Wiener Process for modelling degradation paths. In partial step-stress loading, the unit is tested at usual stress for some time and then stress is accelerated. This helps in preventing over-stressing the test specimens. Failure occurs when the performance characteristic crosses...

Let Z be the Rosenblatt process with the representation Z t = ∫ t

This paper is devoted to a construction of the stochastic Itô integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The connection of the introduced integral with the integral defined by Walsh [9] is provided as well.

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Let W be a real-valued Wiener process starting from 0, and τ(t) be the right-continuous inverse process of its local time at 0. Földes and Puri [3] raise the problem of studying the almost sure asymptotic behavior of X(t) = ∫ τ(t) 0 1l{|W (u)|≤αt}du as t tends to infinity, i.e. they ask: how long does W stay in a tube before “crossing very much” a given level? In this note, both limsup and limi...

While there is growing interest in in-line measurements of paper making processes, the factory environment often restricts the acquisition of images. The in-line imaging of pulp suspension is often difficult due to constraints to camera and light positioning, resulting in images with uneven illumination and motion blur. This article presents an algorithm for segmenting fibers from suspension im...