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- W2206914911 abstract "The main objective of computational probability is the development of algorithms that can provide numerical solutions to problems arising in a stochastic context. These algorithms must provide results within a reasonable computation time and they should also minimize the rounding errors. This chapter describes computational methods that are used for stochastic models. The chapter also discusses algorithms for the transient and steady-state probabilities of discrete-time and continuous-time Markov chains, and for the steady-state probabilities of semi-Markov processes. Phase-type distributions, which are used extensively in algorithmic work, are introduced in the chapter. Ways to generate and store transition matrices, iterative methods (Jacobi and Gauss–Seidel), and aggregation–disaggregation methods that can handle large problems are discussed in the chapter. Markov chains where the rows of the transition matrix repeat are discussed. This structure appears in many queueing models, and several ways of exploiting it are described in the chapter. These include the classic method based on Rouché's theorem, Wiener–Hopf factorization, the matrix methods pioneered by M. Neuts, and the state reduction." @default.
- W2206914911 created "2016-06-24" @default.
- W2206914911 creator A5025740421 @default.
- W2206914911 date "1990-01-01" @default.
- W2206914911 modified "2023-09-27" @default.
- W2206914911 title "Chapter 5 Computational methods in probability theory" @default.
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- W2206914911 doi "https://doi.org/10.1016/s0927-0507(05)80169-0" @default.
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