Stochastic process

About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.

Economic Load Dispatch Constrained by Wind Power Availability: A Wait-and-See Approach

Abstract: In this paper a load dispatch model for the system consisting of both thermal generators and wind turbines is developed. The stochastic wind power is included in the model as a constraint. It is shown that, under certain conditions, the presented model has a set of closed-form solutions. The availability of closed-form solutions is helpful to gain more fundamental insights, such as the impact of a particular parameter on the optimal solution. Moreover, the feasible ranges of optimal solutions are given in the case that the output power of thermal turbines is restricted. Furthermore, the probability distribution and the average of solutions are derived. This is called the wait-and-see approach in the discipline of stochastic programming. The present work shows that the effects of random wind speed on the generated power can be readily assessed.

New insights from a fixed point analysis of single cell IEEE 802.11 WLANs

Abstract: We study a fixed point formalisation of the well known analysis of Bianchi. We provide a significant simplification and generalisation of the analysis. In this more general framework, the fixed point solution and performance measures resulting from it are studied. Uniqueness of the fixed point is established. Simple and general throughput formulas are provided. It is shown that the throughput of any flow will be bounded by the one with the smallest transmission rate. The aggregate throughput is bounded by the reciprocal of the harmonic mean of the transmission rates. In an asymptotic regime with a large number of nodes, explicit formulas for the collision probability, the aggregate attempt rate and the aggregate throughput are provided. The results from the analysis are compared with ns2 simulations, and also with an exact Markov model of the back-off process. It is shown how the saturated network analysis can be used to obtain TCP transfer throughputs in some cases.

Generalized stochastic subdivision

Abstract: Stochastic techniques have assumed a prominent role in computer graphics because of their success in modeling a variety of complex and natural phenomena. This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct high-quality random functions, including those with non-fractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique.

A Stochastic Sampled-Data Approach to Distributed $H_{\infty }$ Filtering in Sensor Networks

Abstract: In this paper, the problem of distributed H∞ filtering in sensor networks using a stochastic sampled-data approach is investigated. A set of general nonlinear equations described by sector-bounded nonlinearities is utilized to model the system and sensors in networks. Each sensor receives the information from both the system and its neighbors. The signal received by each sensor is sampled by a sampler separately with stochastic sampling periods before it is employed by the corresponding filter. By converting the sampling periods into bounded time-delays, the design problem of the stochastic sampled-data based distributed H∞ filters amounts to solving the H∞ filtering problem for a class of stochastic nonlinear systems with multiple bounded time-delays. Then, by constructing a new Lyapunov functional and employing both the Gronwall's inequality and the Jenson integral inequality, a sufficient condition is derived to guarantee the H∞ performance as well as the exponential mean-square stability of the resulting filtering error dynamics. Subsequently, the desired sampled-data based distributed H∞ filters are designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed sampled-data distributed H∞ filtering scheme.