Topic
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.
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TL;DR: In this article, a stochastic wind power model based on an autoregressive integrated moving average (ARIMA) process is proposed to take into account the nonstationarity and physical limits of wind power generation.
Abstract: This paper proposes a stochastic wind power model based on an autoregressive integrated moving average (ARIMA) process. The model takes into account the nonstationarity and physical limits of stochastic wind power generation. The model is constructed based on wind power measurement of one year from the Nysted offshore wind farm in Denmark. The proposed limited-ARIMA (LARIMA) model introduces a limiter and characterizes the stochastic wind power generation by mean level, temporal correlation and driving noise. The model is validated against the measurement in terms of temporal correlation and probability distribution. The LARIMA model outperforms a first-order transition matrix based discrete Markov model in terms of temporal correlation, probability distribution and model parameter number. The proposed LARIMA model is further extended to include the monthly variation of the stochastic wind power generation.
305 citations
Book•
01 Jan 1979
TL;DR: In this article, a discrete-parameter controlled stochastic process is proposed to solve the optimization problem of continuous-time control of Markov chains with incomplete observations, where the objective is to find the optimal stopping point of the Markov chain.
Abstract: 1 Discrete-Parameter Controlled Stochastic Processes.- 1 Definitions.- 2 Optimization Problem.- 3 Construction of Optimal and ?-Optimal Controls.- 4 Control of Processes with Incomplete Observations.- 5 Optimal Stopping Problems.- 6 Controlled Markov Chains.- 7 Homogeneous Controlled Markov Chains.- 8 Optimal Stopping of Markov Chains.- 2 Continuous-Time Control Processes.- 1 General Definitions.- 2 Representation of the Controlled Objects and Construction of Controlled Processes.- 3 Optimization Problem Approximation Theorem.- 4 Controlled Markov Processes.- 5 Jump Markovian Controlled Processes.- 3 Controlled Stochastic Differential Equations.- 1 Some Preliminaries.- 2 Stochastic Differential Equations.- 3 Controlled Stochastic Differential Equations.- 4 Evolutional Loss Functions.- 5 Linear Systems without an After-effect.- 6 Control Equations with Continuous Noise.- 7 Controlled Diffusion Processes.- Historical and Bibliographical Remarks.
304 citations
TL;DR: In this article, the problem of power spectral analysis for non-stationary processes is discussed from the point of view of physical and engineering applications, with emphasis on defining a nonstationary spectrum whose physical interpretation is similar to that of a stationary spectrum.
303 citations
24 Sep 2000
TL;DR: A simple framework for Monte Carlo simulations of a multiple-input-multiple-output radio channel is proposed and it is demonstrated that the Shannon capacity of the channel is highly dependent on the considered environment.
Abstract: A simple framework for Monte Carlo simulations of a multiple-input-multiple-output radio channel is proposed. The derived model includes the partial correlation between the paths in the channel, as well as fast fading and time dispersion. The only input parameters required for the model are the shape of the power delay spectrum and the spatial correlation functions at the transmit and receive end. Thus, the required parameters are available in the open literature for a large variety of environments. It is furthermore demonstrated that the Shannon capacity of the channel is highly dependent on the considered environment.
302 citations
TL;DR: This work considers stochastic vehicle routing problems on a network with random travel and service times and provides bounds on optimal objective function values and conditions under which reductions to simpler models can be made.
Abstract: We consider stochastic vehicle routing problems on a network with random travel and service times. A fleet of one or more vehicles is available to be routed through the network to service each node. Two versions of the model are developed based on alternative objective functions. We provide bounds on optimal objective function values and conditions under which reductions to simpler models can be made. Our solution method embeds a branch-and-cut scheme within a Monte Carlo sampling-based procedure.
302 citations