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Home Learning. Notify me. Description From the Introduction: " The emphasis has been placed on topics of interest in systems science at large The level of exposition and the inclusion of a large number of exercises with complete detailed solutions make this book usable as a text for graduate students in applied probability, electrical engineering, computer science, and operations research. The prerequisites in probability and random processes are recalled in the Appendices. Other books in this series.
Add to basket. Advances in Physical Geochemistry Surendra K. Physical Chemistry of Magmas Leonid L. Kinetics and Equilibrium in Mineral Reactions S. Metamorphic Reactions B. Thermodynamics of Minerals and Melts R. Table of contents I Martingales. Histories and Stopping Times. Square-Integrable Martingales. Counting Processes and Queues.
Watanabe's Characterization. Stochastic Intensity, General Case. Predictable Intensities. Representation of Queues. Random Changes of Time. Cryptographic Point Processes. The Structure of Internal Histories. Regenerative Form of the Intensity. The Representation Theorem.
Hilbert-Space Theory of Poissonian Martingales. Useful Extensions. The Theory of Innovations. State Estimates for Queues and Markov Chains. Continuous States and Nontrivial Prehistory. Jackson's Networks. Burke's Output Theorem for Networks. Cascades and Loops in Jackson's Networks.
Independence and Poissonian Flows in Markov Chains. Radon-Nikodym Derivatives and Tests of Hypotheses. Changes of Intensities "a la Girsanov". Filtering by the Method of the Probability of Reference.
The Capacity of a Point-Process Channel. Modeling Intensity Controls. Input Regulation. A Case Study in Impulsive Control. Attraction Controls. Existence via Likelihood Ratio. Counting Measure and Intensity Kernels.
Martingale Representation and Filtering. Radon-Nikodym Derivatives. Towards a General Theory of Intensity. Monotone Class Theorem. Random Variables. Conditioning and Independence. Stochastic Processes. Markov Processes. Stopping Times. Point-Process Histories. Ito's Stochastic Integral. Square-Integrable Brownian Martingales. Girsanov's Theorem. The Stieltjes-Lebesgue Integral. The Product and Exponential Formulas.
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Point process models are employed in many areas of applied mathematics. Generally these are of fairly simple structure, being derived from basic Poisson or renewal processes. Recently, however, more sophisticated models have been introduced, based on the rapidly-growing theory of martingales and stochastic calculus, The books of Liptser and Shiryaev  and Elliott  can be consulted for a full account of this theory. Unable to display preview. Download preview PDF.
The Martingale Theory of Point Processes and its Application to the Analysis of Failure-Time Data