Lectures on the Poisson Process

Mathew Penrose, Günter Last

ISBN 10: 1107458439 / ISBN 13: 9781107458437

Editore: Cambridge University Press, GB, 2017

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The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.

Codice articolo LU-9781107458437

Dati bibliografici

• Titolo: Lectures on the Poisson Process
• Editore: Cambridge University Press, GB
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 1107458439
• ISBN 13: 9781107458437
• Rilegatura: Paperback
• Condizione: New
• Peso: 460 grammi

Descrizione articolo

Riassunto

A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

Informazioni sugli autori

Günter Last is Professor of Stochastics at the Karlsruhe Institute of Technology, Germany. He is a distinguished probabilist with particular expertise in stochastic geometry, point processes, and random measures. He coauthored a research monograph on marked point processes on the line as well as two textbooks on general mathematics. He has given many invited talks on his research worldwide.

Mathew Penrose is Professor of Probability at the University of Bath. He is an internationally leading researcher in stochastic geometry and applied probability and is the author of the influential monograph Random Geometric Graphs (2003). He received the Friedrich Wilhelm Bessel Research Award from the Humboldt Foundation in 2008, and has held visiting positions as guest lecturer in New Delhi, Karlsruhe, San Diego, Birmingham, and Lille.