Stochastic processes [[electronic resource] /] / J. Medhi

• Record Nr.: UNINA9910785886903321
• Autore: Medhi J (Jyotiprasad)
• Pubbl/distr/stampa: Tunbridge Wells, UK, : New Academic Science Limited, c2012
• ISBN: 1-906574-65-0
• Edizione: [3rd ed.]
• Descrizione fisica: 1 online resource (518 p.)
• Soggetti: Stochastic processes; Probabilities
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: ""Cover""; ""Preface to the International Edition ""; ""Contents ""; ""Chapter 1 Random Variables and Stochastic Processes ""; ""1.1 Generating Functions ""; ""1.1.1 Introduction""; ""1.1.2 Probability Generating Function: Mean and Variance""; ""1.1.3 Sum of (a Fixed Number of) Random Variables""; ""1.1.4 Sum of a Random Number of Discrete Random Variables (Stochastic Sum)""; ""1.1.5 Generating Function of Bivariate Distribution""; ""1.2 Laplace Transform ""; ""1.2.1 Introduction""; ""1.2.2 Some Important Properties of Laplace Transforms: see Appendix A1""; ""1.2.3 Inverse Laplace Transform""; ""1.3 Laplace (Stieltjes) Transform of a Probability Distribution or of a Random Variable """"1.3.1 Definition""; ""1.3.2 The Laplace Transform of the Distribution Function in Terms of that of the Density Function ""; ""1.3.3 Mean and Variance in Terms of (Derivatives of) L.T.""; ""1.3.4 Some Important Distributions""; ""1.3.5 Three Important Theorems""; ""1.3.6 Geometric and Exponential Distributions""; ""1.3.7 Sum of a Random Number of Continuous Random Variables Stochastic Î?m""; ""1.3.8 Randomization and Mixtures""; ""1.4 Classification of Distributions ""; ""1.4.1 Hazard (or Failure) Rate Function""""1.4.2 Mean Residual Life (MRL)""; ""1.4.3 Further Properties""; ""1.5 Stochastic Processes: An Introduction ""; ""1.5.1 Specification of Stochastic Processes""; ""Exercises ""; ""References ""; ""Chapter 2 Markov Chains ""; ""2.1 Definition and Examples ""; ""2.1.1 Transition Matrix (or Matrix of Transition Probabilities""; ""2.1.2 Order of a Markov Chain""; ""2.1.3 ; Markov Chains as Graphs""; ""2.2 Higher Transition Probabilities ""; ""2.3 Generalisation of Independent Bernoulli Trials: Sequence of Chain-Dependent Trials ""; ""2.3.1 Markov-Bernoulli Chain""""2.3.2 Correlated Random Walk ""; ""2.4 Classification of States and Chains ""; ""2.4.1 Communication Relations""; ""2.4.2 Class Property""; ""2.4.3 Classification of Chains""; ""2.4.4 Classification of States: Transient and Persistent (Recurrent) States""; ""2.5 Determination of Higher Transition Probabilities ""; ""2.5.1 Aperiodic Chain: Limiting Behaviour""; ""2.6 Stability of a Markov System ""; ""2.6.1 Computation of the Equilibrium Probabilities""; ""2.7 Graph Theoretic Approach ""; ""2.8 Markov Chain With Denumerable Number of States (Or Countable State Space) """"2.9 Reducible Chains ""; ""2.9.1 Finite Reducible Chains with a Single Closed Class""; ""2.9.2 Chain with One Single Class of Persistent Non-null Aperiodic States""; ""2.9.3 Absorbing Markov Chains""; ""2.9.4 Extension: Reducible Chain with one Closed Class of Persistent Aperiodic States""; ""2.9.5 Further Extension: Reducible Chains with more than one Closed Class""; ""2.10 Statistical Inference for Markov Chains ""; ""2.10.1 M.L. Estimation and Hypothesis Testing""; ""2.10.2 Determination of the Order of a Markov Chain by MAICE""