Author | Khoshnevisan, Davar. author |
---|---|

Title | Multiparameter Processes [electronic resource] : An Introduction to Random Fields / by Davar Khoshnevisan |

Imprint | New York, NY : Springer New York : Imprint: Springer, 2002 |

Connect to | http://dx.doi.org/10.1007/b97363 |

Descript | XX, 584 p. 8 illus. online resource |

SUMMARY

Multiparameter processes extend the existing one-parameter theory of random processes in an elegant way, and have found connections to diverse disciplines such as probability theory, real and functional analysis, group theory, analytic number theory, and group renormalization in mathematical physics, to name a few. This book lays the foundation of aspects of the rapidly-developing subject of random fields, and is designed for a second graduate course in probability and beyond. Its intended audience is pure, as well as applied, mathematicians. Davar Khoshnevisan is Professor of Mathematics at the University of Utah. His research involves random fields, probabilistic potential theory, and stochastic analysis

CONTENT

Discrete-Parameter Random Fields -- Discrete-Parameter Martingales -- Two Applications in Analysis -- Random Walks -- Multiparameter Walks -- Gaussian Random Variables -- Limit Theorems -- Continuous-Parameter Random Fields -- Continuous-Parameter Martingales -- Constructing Markov Processes -- Generation of Markov Processes -- Probabilistic Potential Theory -- Multiparameter Markov Processes -- The Brownian Sheet and Potential Theory

Mathematics
Functional analysis
Probabilities
Mathematics
Probability Theory and Stochastic Processes
Functional Analysis