Probability Theory And Stochastic Processes

by Krzysztof Debicki (Author), Michel Mandjes (Author)
Combines Lévy-based fluctuation theory and queueing theory

This book presents applied probability and stochastic processes in an elementary but mathematically precise manner, with numerous examples and exercises to illustrate the range of engineering and science applications of the concepts. The book is designed to give the reader an intuitive understanding of probabilistic reasoning, in addition to an understanding of mathematical concepts and principles. The initial chapters present a summary of probability and statistics and then Poisson processes, Markov chains, Markov processes and queuing processes are introduced. Advanced topics include simulation, inventory theory, replacement theory, Markov decision theory, and the use of matrix geometric procedures in the analysis of queues.

by Wei Liu (Author), Michael Röckner (Author)
A concise and as self-contained as possible introduction to the ‘variational approach’ of SPDEs
Provides a very detailed introduction to stochastic integration on Hilbert spaces
Includes a complete proof of the finite-dimensional case using the Euler approximation