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: It is shown how, in the collocated case, more accurate results can be obtained with the augmented filter due to its incorporation of modeling errors, while better solutions are produced by classical deterministic methods as Dynamic Programming in which only the forces are estimated, and not the states as well.
327 citations
Book•
01 Jan 1972
TL;DR: This text provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research.
Abstract: Ross's classic bestseller, Introduction to Probability Models, has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries. A new section (3.7) on COMPOUND RANDOM VARIABLES, that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions. A new section (4.11) on HIDDDEN MARKOV CHAINS, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states. Simplified Approach for Analyzing Nonhomogeneous Poisson processes Additional results on queues relating to the (a) conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system; (b) inspection paradox for M/M/1 queues (c) M/G/1 queue with server breakdown Many new examples and exercises.
326 citations
TL;DR: In this paper, a simple solvable "stochastic volatility" model for return fluctuations is proposed, which is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics.
Abstract: In this paper, we provide a simple, "generic"interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as recently observed in reference [23], naturally emerge. We then propose a simple solvable "stochastic volatility"model for return fluctuations. This model is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics. Moreover, its extension to a multivariate context, in order to model portfolio behavior, is very natural. Comparisons to real data and other models proposed elsewhere are provided.
326 citations
01 Jan 1981
TL;DR: In this article, a technique for calculating organized structures in turbulent shear flows is proposed, based on a homogeneous function decomposition and involves representation of a random function as a series of coherent structures occurring at stochastic locations with sparsity.
Abstract: A technique is proposed for calculating organized structures in turbulent shear flows. The proposed approach is based on a homogeneous function decomposition and involves representation of a random function as a series of coherent structures occurring at stochastic locations with stochastic strengths. Attention is given to the retrieval of phase information and information on overlap and spacing, nearly parallel shear flows, dynamical equations, and applications to measurements.
325 citations
TL;DR: It is shown how the wavelet transform directly suggests a modeling paradigm for multiresolution stochastic modeling and related notions of multiscale stationarity in which scale plays the role of a time-like variable.
Abstract: An overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing. A natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image. In particular, it is shown how the wavelet transform directly suggests such a modeling paradigm. This perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time-like variable. The investigation of models on homogeneous trees is emphasized. The framework examined here allows for consideration, in a very natural way, of the fusion of data from sensors with differing resolutions. Also, thanks to the fact that wavelet transforms do an excellent job of 'compressing' large classes of covariance kernels, it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect. >
325 citations