The Wiener disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of ’disorder’ when the drift of an observed Wiener process changes from one value to another. In this paper we present a solution of the Wiener disorder problem when the horizon is finite. The method of proof is based on reducing the initial problem to a parabolic free-boundary pro...

Sampling is a very important and basic technique for signal processing. In the case that noise is added to a signal in the sampling process, we may use a reconstruction and noise reduction filter such as the Wiener filter. The Wiener filter provides a restored signal of which mean square error is minimized. However, the mean square error by the Wiener filter depends on the sampling vectors. We ...

Coagulation process control is an essential operation in water treatment plants. It is a challenging control problem due to the nonlinear and physicochemical nature of the coagulation process. The paper presents the application of the Wiener model predictive control (WMPC) algorithm to a coagulation chemical dosing unit for water treatment plants in order to keep the surface charge and pH level...

We consider a time varying wireless fading channel, equalized by an LMS Decision Feedback equalizer (DFE). We study how well this equalizer tracks the optimal MMSEDFE (Wiener) equalizer. We model the channel by an Autoregressive (AR) process. Then the LMS equalizer and the AR process are jointly approximated by the solution of a system of ODEs (ordinary differential equations). Using these ODEs...

Wiener process with a linear drift has been extensively studied in degradation modeling, mainly due to the existence of an analytical expression of the first hitting time distribution which permits feasible mathematical developments. However, a fundamental problem related to the stationary Wiener process is that it can only describe linearly drifted diffusion processes. This article is devoted ...

We develop a completely new and straightforward method for simulating the joint law of the position and running maximum at a fixed time of a general Lévy process with a view to application in insurance and financial mathematics. Although different, our method takes lessons from Carr’s so-called “Canadization” technique as well as Doney’s method of stochastic bounds for Lévy processes; see Carr ...