An Introduction to Applied Probability
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Beschreibung
This book provides the elements of probability and stochastic processes of direct interest to the applied sciences where probabilistic models play an important role, most notably in the information and communications sciences, computer sciences, operations research, and electrical engineering, but also in fields like epidemiology, biology, ecology, physics, and the earth sciences.
The theoretical tools are presented gradually, not deterring the readers with a wall of technicalities before they have the opportunity to understand their relevance in simple situations. In particular, the use of the so-called modern integration theory (the Lebesgue integral) is postponed until the fifth chapter, where it is reviewed in sufficient detail for a rigorous treatment of the topics of interest in the various domains of application listed above.
The treatment, while mathematical, maintains a balance between depth and accessibility that is suitable for the efficient manipulation, based on solid theoretical foundations, of the four most important and ubiquitous categories of probabilistic models:
- Markov chains, which are omnipresent and versatile models in applied probability
- Poisson processes (on the line and in space), occurring in a range of applications from ecology to queuing and mobile communications networks
- Brownian motion, which models fluctuations in the stock market and the "white noise" of physics
- Wide-sense stationary processes, of special importance in signal analysis and design, as well as in the earth sciences.
This book provides the elements of probability and stochastic processes of direct interest to the applied sciences where probabilistic models play an important role, most notably in the information and communications sciences, computer sciences, operations research, and electrical engineering, but also in fields like epidemiology, biology, ecology, physics, and the earth sciences.
The theoretical tools are presented gradually, not deterring the readers with a wall of technicalities before they have the opportunity to understand their relevance in simple situations. In particular, the use of the so-called modern integration theory (the Lebesgue integral) is postponed until the fifth chapter, where it is reviewed in sufficient detail for a rigorous treatment of the topics of interest in the various domains of application listed above.
The treatment, while mathematical, maintains a balance between depth and accessibility that is suitable for theefficient manipulation, based on solid theoretical foundations, of the four most important and ubiquitous categories of probabilistic models:
- Markov chains, which are omnipresent and versatile models in applied probability
- Poisson processes (on the line and in space), occurring in a range of applications from ecology to queuing and mobile communications networks
- Brownian motion, which models fluctuations in the stock market and the "white noise" of physics
- Wide-sense stationary processes, of special importance in signal analysis and design, as well as in the earth sciences.
Provides a clear and intuitive introduction to the range of probabilistic tools used in the applied sciences Covers diverse topics such as random graphs, rejection sampling, and Bayesian hypothesis testing Includes lots of exercises for practice and homework
Autor*in
Pierre Brémaud
Themen in »An Introduction to Applied Probability«
Probability textbook Markov chains Discrete random variables Random vectors Convergence of random variables Conditional expectation Continuous-time stochastic processes Brownian motion Wiener process Stochastic integral Markov fields Simulation algorithm Poisson processes Wide-sense stationary processes Martingales