03396nam 22005293 450 991101963710332120241023080342.097811194198081119419808978139432990813943299039781394329892139432989X(MiAaPQ)EBC31733451(Au-PeEL)EBL31733451(CKB)36378994000041(Exl-AI)31733451(Perlego)4605941(EXLCZ)993637899400004120241023d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierPhase Type Distributions, Volume 2 Theory and Application1st ed.Newark :John Wiley & Sons, Incorporated,2022.©2024.1 online resource (280 pages)9781848219458 1848219458 Cover -- TTitle Page -- Copyright Page -- Contents -- Introduction -- Chapter 1. Mathematical Background -- 1.1. Basic properties of random variables -- 1.2. Moments of random variables and related quantities -- 1.3. Laplace transformation -- 1.4. z transform -- 1.5. Matrix functions of quadratic matrices -- 1.6. Matrix inverse -- 1.7. Eigenvalues and the characteristic polynomial -- 1.8. Spectral decomposition -- 1.9. Ordinary differential equation of vector functions -- 1.10. Exponential distribution -- 1.11. Erlang distribution -- 1.12. Discrete time Markov chain -- 1.13. Continuous time Markov chain -- 1.14. Kronecker algebra -- Chapter 2. Continuous Phase Type Distributions -- 2.1. Definition and basic properties -- 2.2. Stochastic meaning of (-A)-1 -- 2.3. Rational Laplace transform -- 2.4. Decomposition of matrix exponential functions -- 2.5. Similarity transformation -- 2.5.1. Similarity transformation with identical sizes -- 2.5.2. Similarity transformation with different sizes -- 2.5.3. Full rank representation -- 2.6. Closure propertiesGenerated by AI.This book, authored by András Horváth and Miklós Telek, delves into the theoretical foundations and applications of phase type distributions in stochastic models, with a particular focus on computer science and network systems. It presents a comprehensive overview of mathematical concepts such as random variables, matrix functions, Markov chains, and differential equations, essential for understanding phase type distributions. The authors aim to provide readers with a detailed understanding of both continuous and discrete phase type distributions, their properties, and applications. This work is intended for researchers, academics, and professionals in the fields of mathematics, computer science, and engineering who are interested in stochastic modeling and its applications.Generated by AI.Stochastic processesGenerated by AIMathematical modelsGenerated by AIStochastic processesMathematical modelsHorváth András1763665Telek Miklós781358MiAaPQMiAaPQMiAaPQBOOK9911019637103321Phase Type Distributions, Volume 24420638UNINA