This book gives a self-contained introduction to the dynamic martingale approach to marked point processes (MPP). Based on the notion of a compensator, this approach gives a versatile tool for analyzing and describing the stochastic properties of an MPP. In particular, the authors discuss the relationship of an MPP to its compensator and particular classes of MPP are studied in great detail. The theory is applied to study properties of dependent marking and thinning, to prove results on absolute continuity of point process distributions, to establish sufficient conditions for stochastic ordering between point and jump processes, and to solve the filtering problem for certain classes of MPPs.
Marked Point Processes on the Real Line
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"It is obvious that the authors have had fun in writing this book; they want to share their enthusiasm for the subject with a broad readership...The authors are to be congratulated on the final product." (International Statistical Institute short book reviews)
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Inside This Book
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First Sentence:
A point process is a sequence of random variables Tn satisfying Tn Tn+1. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
canonical compensator, stochastic intensity kernel, closed partial ordering, mixed sample process, point process filtrations, univariate point process, predictable kernel, point process martingales, point process distributions, predictable random measure, predictable stopping time, predictable projection, intensity kernels, successive conditioning, delayed renewal process, stochastic kernel, stochastic intensities, independent random elements, monotone class theorem, optional projections, martingale characterization, marked point process, hazard measure, independent marking, predictable version Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Theorem, Representation of Jump Processes New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A point process is a sequence of random variables Tn satisfying Tn Tn+1. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
canonical compensator, stochastic intensity kernel, closed partial ordering, mixed sample process, point process filtrations, univariate point process, predictable kernel, point process martingales, point process distributions, predictable random measure, predictable stopping time, predictable projection, intensity kernels, successive conditioning, delayed renewal process, stochastic kernel, stochastic intensities, independent random elements, monotone class theorem, optional projections, martingale characterization, marked point process, hazard measure, independent marking, predictable version Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Theorem, Representation of Jump Processes New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 27
books:
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- Random Point Processes by Donald L. Snyder in Back Matter
- Limit Theorems for Stochastic Processes by Jean Jacod in Back Matter
- Introduction to Stochastic Processes by Erhan Cinlar in Back Matter
- Regeneration and Networks of Queues (Applied Probability) (v. 3) by Gerald S. Shedler in Front Matter
- Probabilistic Techniques in Analysis (Probability and Its Applications) by Richard F. Bass in Front Matter
See all 27 books this book cites
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