Probability and stochastic modeling. (2012)

• Record Type: Book
• Further Information: Note: Vladimir I. Rotar.
• Other Names: Rotarʹ, V. I (Vladimir Ilʹich)
• Contents: Basic Notions; Sample Space and Events; Probabilities; Counting Techniques Independence and Conditional Probability ; Independence; Conditioning; The Borel-Cantelli Theorem Discrete Random Variables; Random Variables and Vectors; Expected Value; Variance and Other Moments. Inequalities for Deviations; Some Basic Distributions; Convergence of Random Variables. The Law of Large Numbers; Conditional Expectation Generating Functions. Branching Processes. Random Walk Revisited ; Branching Processes; Generating Functions; Branching Processes Revisited; More on Random Walk Markov Chains ; Definitions and Examples. Probability Distributions of Markov Chains; The First Step Analysis. Passage Times; Variables Defined on a Markov Chain; Ergodicity and Stationary Distributions; A Classification of States and Ergodicity Continuous Random Variables ; Continuous Distributions; Some Basic Distributions; Continuous Multivariate Distributions; Sums of Independent Random Variables; Conditional Distributions and Expectations Distributions in the General Case. Simulation ; Distribution Functions; Expected Values; On Convergence in Distribution and Probability; Simulation; Histograms Moment Generating Functions ; Definitions and Properties; Some Examples of Applications; Exponential or Bernstein-Chernoff’s Bounds The Central Limit Theorem for Independent Random Variables ; The Central Limit Theorem (CLT) for Independent and Identically Distributed Random Variables; The CLT for Independent Variables in the General Case Covariance Analysis. The Multivariate Normal Distribution. The Multivariate Central Limit Theorem ; Covariance and Correlation; Covariance Matrices and Some Applications; The Multivariate Normal Distribution Maxima and Minima of Random Variables. Elements of Reliability Theory. Hazard Rate and Survival Probabilities; Maxima and Minima of Random Variables. Reliability Characteristics; Limit Theorems for Maxima and Minima; Hazard Rate. Survival Probabilities Stochastic Processes: Preliminaries ; A General Definition; Processes with Independent Increments; Brownian Motion; Markov Processes; A Representation and Simulation of Markov Processes in Discrete Time Counting and Queuing Processes. Birth and Death Processes: A General Scheme; Poisson Processes; Birth and Death Processes Elements of Renewal Theory; Preliminaries; Limit Theorems; Some Proofs Martingales in Discrete Time ; Definitions and Properties; Optional Time and Some Applications; Martingales and a Financial Market Model; Limit Theorems for Martingales Brownian Motion and Martingales in Continuous Time; Brownian Motion and Its Generalizations; Martingales in Continuous Time More on Dependency Structures; Arrangement Structures and the Corresponding Dependencies; Measures of Dependency; Limit Theorems for Dependent Random Variables; Symmetric Distributions. De Finetti’s Theorem Comparison of Random Variables. Risk Evaluation ; Some Particular Criteria; Expected Utility; Generalizations of the EUM Criterion Appendix References Answers to Exercises Index Exercises appear at the end of each chapter.
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2012
• Extent: 1 online resource (508 pages), (16 illustrations)
• Subjects: 519.2; Probabilities; Stochastic models
• Languages: English
• ISBNs: 9781439872079; 1439872074
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.