LEADER 03396nam 22005293 450 001 9911019637103321 005 20241023080342.0 010 $a9781119419808 010 $a1119419808 010 $a9781394329908 010 $a1394329903 010 $a9781394329892 010 $a139432989X 035 $a(MiAaPQ)EBC31733451 035 $a(Au-PeEL)EBL31733451 035 $a(CKB)36378994000041 035 $a(Exl-AI)31733451 035 $a(Perlego)4605941 035 $a(EXLCZ)9936378994000041 100 $a20241023d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPhase Type Distributions, Volume 2 $eTheory and Application 205 $a1st ed. 210 1$aNewark :$cJohn Wiley & Sons, Incorporated,$d2022. 210 4$d©2024. 215 $a1 online resource (280 pages) 311 08$a9781848219458 311 08$a1848219458 327 $aCover -- 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 properties$7Generated by AI. 330 $aThis 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.$7Generated by AI. 606 $aStochastic processes$7Generated by AI 606 $aMathematical models$7Generated by AI 615 0$aStochastic processes 615 0$aMathematical models 700 $aHorváth$b András$01763665 701 $aTelek$b Miklós$0781358 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019637103321 996 $aPhase Type Distributions, Volume 2$94420638 997 $aUNINA