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.

Analysis of random processes via And-Or tree evaluation

Abstract: We introduce a new set of probabilistic analysis tools based on the analysis of And-Or trees with random inputs. These tools provide a unifying, intuitive, and powerful framework for carrying out the analysis of several previously studied random processes of interest, including random loss-resilient codes, solving random k-SAT formula using the pure literal rule, and the greedy algorithm for matchings in random graphs. In addition, these tools allow generalizations of these problems not previously analyzed to be analyzed in a straightforward manner. We illustrate our methodology on the three problems listed above

Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing

Abstract: Customary modeling for continuous point-referenced data assumes a Gaussian process that is often taken to be stationary. When such models are fitted within a Bayesian framework, the unknown parameters of the process are assumed to be random, so a random Gaussian process results. Here we propose a novel spatial Dirichlet process mixture model to produce a random spatial process that is neither Gaussian nor stationary. We first develop a spatial Dirichlet process model for spatial data and discuss its properties. Because of familiar limitations associated with direct use of Dirichlet process models, we introduce mixing by convolving this process with a pure error process. We then examine properties of models created through such Dirichlet process mixing. In the Bayesian framework, we implement posterior inference using Gibbs sampling. Spatial prediction raises interesting questions, but these can be handled. Finally, we illustrate the approach using simulated data, as well as a dataset involving precipitati...

Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems.

Abstract: Comprehensive uncertainty analyses of complex models of environmental and biological systems are essential but often not feasible due to the computational resources they require. "Traditional" methods, such as standard Monte Carlo and Latin Hypercube Sampling, for propagating uncertainty and developing probability densities of model outputs, may in fact require performing a prohibitive number of model simulations. An alternative is offered, for a wide range of problems, by the computationally efficient "Stochastic Response Surface Methods (SRSMs)" for uncertainty propagation. These methods extend the classical response surface methodology to systems with stochastic inputs and outputs. This is accomplished by approximating both inputs and outputs of the uncertain system through stochastic series of "well behaved" standard random variables; the series expansions of the outputs contain unknown coefficients which are calculated by a method that uses the results of a limited number of model simulations. Two case studies are presented here involving (a) a physiologically-based pharmacokinetic (PBPK) model for perchloroethylene (PERC) for humans, and (b) an atmospheric photochemical model, the Reactive Plume Model (RPM-IV). The results obtained agree closely with those of traditional Monte Carlo and Latin Hypercube Sampling methods, while significantly reducing the required number of model simulations.

Stochastic resonance on a circle.

Abstract: We describe a new realization of stochastic resonance, applicable to a broad class of systems, based on an underlying excitable dynamics with deterministic reinjection. A simple but general theory of such ``single-trigger'' systems is compared with analog simulations of the Fitzhugh-Nagumo model, as well as experimental data obtained from stimulated sensory neurons in the crayfish.

Probability, random processes, and ergodic properties

Abstract: Probability, Random Processes, and Ergodic Properties is for mathematically inclined information/communication theorists and people working in signal processing. It will also interest those working with random or stochastic processes, including mathematicians, statisticians, and economists. Highlights Second edition of classic text Complete tour of book and guidelines for use given in Introduction, so readers can see at a glance the topics of interest Structures mathematics for an engineering audience, with emphasis on engineering applications. New in the Second Edition Much of the material has been rearranged and revised for pedagogical reasons. The original first chapter has been split in order to allow a more thorough treatment of basic probability before tackling random processes and dynamical systems. The final chapter has been broken into two pieces to provide separate emphasis on process metrics and the ergodic decomposition of affine functionals. Completion of event spaces and probability measures is treated in more detail. More specific examples of random processes have been introduced. Many classic inequalities are now incorporated into the text, along with proofs; and many citations have been added. From the Authors Preface... This book has a long history. It began over two decades ago as the first half of a book on information and ergodic theory. The intent was and remains to provide a reasonably self-contained advanced (at least for engineers) treatment of measure theory, probability theory, and random processes, with an emphasis on general alphabets and on ergodic and stationary properties of random processes that might be neither ergodic nor stationary. The intended audience was mathematically inclined engineers who had not had formal courses in measure theoretic probability or ergodic theory. Much of the material is familiar stuff for mathematicians, but many of the topics and results had not then previously appeared in books. The original project grew too large and the first part contained much that would likely bore mathematicians and discourage them from the second part. Hence I finally followed a suggestion to separate the material and split the project in two. The resulting manuscript fills a unique hole in the literature. Personal experience indicates that the intended audience rarely has the time to take a complete course in measure and probability theory in a mathematics or statistics department, at least not before they need some of the material in their research. I intended in this book to provide a catalogue of many results that I have found need of in my own research together with proofs that I could follow. I also intended to clarify various connections that I had found confusing or insufficiently treated in my own reading. If the book provides similar service for others, it will have succeeded.