Modeling the Energy Harvested by an RF Energy Harvesting System Using Gamma Processes

In an Energy Harvesting system (EHS) the gamma process is used to model the electromagnetic energy received from radiofrequency (RF) radiation. The stochastic characterization of the harvested energy as a continuous-time stochastic process, namely, gamma process, is obtained from the Nakagami-m fading model, which describes the signal reception in a large amount of types of radiofrequency channels. Using the gamma process, some performance measures of the EHS system are obtained. Also, a transmission policy subject to different fading conditions is considered.

Stochastic Process Models of Preference Change

This chapter gives an informal summary of a research program aiming to develop and test stochastic process models of preference change. What does it take to develop a formally precise and descriptively valid model of persuasion? Any such model should specify formally concise definitions of hypothetical constructs such as preferences or attitudes. The chapter reviews weak order and semiorder models of preferences that are grounded in decision theory. Such a model should also spell out how hypothetical constructs relate to observable behavior, such as feeling thermometer ratings. The chapter reviews response processes that, in some cases, accommodate within and across respondent heterogeneity in overt behavior. The model should furthermore specify formally what it means to change one’s preference over time and how that change relates to the persuasive environment. The chapter treats preference change as a continuous time stochastic process on a graph of preference states. The most innovative feature of the approach is to model the (perceived) persuasive environment itself also as a hypothetical construct that is not directly/objectively observable by the researcher. Last but not least, the chapter discusses how to accommodate partisan differences, how to incorporate respondents with immutable preferences, and the possibility that respondents may tune in and out of a persuasive campaign. The emphasis of the chapter lies in explaining key conceptual ideas grounded in decision theory and mathematical psychology.

Asynchronous distributed state estimation for continuous-time stochastic processes

The problem of state estimation of a continuous-time stochastic process using an Asynchronous Distributed multi-sensor Estimation (ADE) system is considered. The state of a process of interest is estimated by a group of local estimators constituting the proposed ADE system. Each estimator is based, e.g., on a Kalman filter and performs single sensor filtration and fusion of its local results with the results from other/remote processors to compute possibly the best state estimates. In performing data fusion, however, two important issues need to be addressed namely, the problem of asynchronism of local processors and the issue of unknown correlation between asynchronous data in local processors. Both the problems, along with their solutions, are investigated in this paper. Possible applications and effectiveness of the proposed ADE approach are illustrated by simulated experiments, including a non-complete connection graph of such a distributed estimation system.

Continuous-Time Skewed Multifractal Processes as a Model for Financial Returns

We present the construction of a continuous-time stochastic process which has moments that satisfy an exact scaling relation, including odd-order moments. It is based on a natural extension of the multifractal random walk construction described in Bacry and Muzy (2003). This allows us to propose a continuous-time model for the price of a financial asset that reflects most major stylized facts observed on real data, including asymmetry and multifractal scaling.

Continuous-Time Skewed Multifractal Processes as a Model for Financial Returns

We present the construction of a continuous-time stochastic process which has moments that satisfy an exact scaling relation, including odd-order moments. It is based on a natural extension of the multifractal random walk construction described in Bacry and Muzy (2003). This allows us to propose a continuous-time model for the price of a financial asset that reflects most major stylized facts observed on real data, including asymmetry and multifractal scaling.

Time-Variant Reliability Assessment and Its Sensitivity Analysis of Cutting Tool under Invariant Machining Condition Based on Gamma Process

The time-variant reliability and its sensitivity of cutting tools under both wear deterioration and an invariant machining condition are analyzed. The wear process is modeled by a Gamma process which is a continuous-state and continuous-time stochastic process with the independent and nonnegative increment. The time-variant reliability and its sensitivity of cutting tools under six cases are considered in this paper. For the first two cases, the compensation for the cutting tool wear is not carried out. For the last four cases, the off-line or real-time compensation method is adopted. While the off-line compensation method is used, the machining error of cutting tool is supposed to be stochastic. Whether the detection of the real-time wear is accurate or not is discussed when the real-time compensation method is adopted. The numerical examples are analyzed to demonstrate the idea of how the reliability of cutting tools under the invariant machining condition could be improved according to the methods described in this paper.