Optimization of stochastic discrete systems and control on complex networks : complex networks /: complex networks. (2015)

• Record Type: Book
• Further Information: Note: Dmitrii Lozovanu, Stefan Pickl.
• Authors: Lozovanu, Dmitrii; Pickl, Stefan
• Contents: Preface; Contents; Notations; 1 Discrete Stochastic Processes, Numerical Methods for Markov Chains and Polynomial Time Algorithms; 1.1 The Basic Definitions and Some Preliminary Results; 1.1.1 Discrete Markov Processes and Determining the State-Time Probabilities of the System; 1.1.2 Definition of the Limit Matrix and the Classification of the States in Markov Chains; 1.1.3 A Decomposition Algorithm for Determining the Limit Matrix; 1.1.4 The z-Transform and the Asymptotic Behavior of State-Time Probabilities; 1.2 An Algorithm for Determining the Limit Matrix. 1.2.1 The Main Approach and the General Scheme of the Algorithm1.2.2 The Calculation of the Coefficients of the Characteristic Polynomial; 1.2.3 Determining the z-Transform Function; 1.2.4 An Algorithm for Calculating the Limit Matrix; 1.3 An Algorithm for Determining the Differential Matrices in Markov Chains; 1.3.1 Determining the Differential Matrices Based on the z-Transform; 1.3.2 Linear Recurrent Equations and its Main Properties; 1.3.3 The Main Results and an Algorithm; 1.3.4 Comments on the Computational Complexity of the Algorithm. 1.4 An Algorithm for Determining the Limit and the Differential Matrices1.4.1 Some Auxiliary Results Concerning the Representation of the z-Transform; 1.4.2 Expansion of the z-Transform with Respect to Nonzero Characteristic Values; 1.4.3 The Main Conclusion and the Description of the Algorithm; 1.4.4 Numerical Examples; 1.5 A Dynamic Programming Approach for Discrete Markov Processes ; 1.5.1 Calculation of the State-Time Probability of the System with the Restriction on the Number of Transitions. 1.5.2 Determining the Limiting State Probabilities in Markov Chains Based on Dynamic Programming1.5.3 An Algorithm for the Calculation of the Limit Matrix in Markov Chains with Running Time O(n3); 1.5.4 An Algorithm for Determining the Limit Probabilities Based on the Ergodicity Condition; 1.5.5 Determining the First Hitting Limiting Probability of the State in a Markov Chain; 1.6 Determining the State-Time Probabilities of the System ; 1.7 Markov Processes with Rewards and Transition Costs; 1.7.1 Definition and Calculation of the Expected Total Cost. 1.7.2 An Asymptotic Behavior Analysis of the Expected Total Cost Based on the z-Transform1.7.3 Determining the Expected Total Cost for Non-stationary Markov Processes; 1.7.4 Definition and Calculation of the Variance of the Total Cost; 1.8 Markov Processes with Discounted Costs; 1.9 Semi-Markov Processes with Transition Costs; 1.10 Determining the Expected Total Cost for Markov Processes with Stopping States; 2 Stochastic Optimal Control Problems and Markov Decision Processes with Infinite Time Horizon.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2015
• Copyright Date: 2015
• Extent: 1 online resource (416 pages), illustrations
• Subjects: 519.233; Business; Markov processes; Dynamic programming; Stochastic control theory; Dynamic programming; Markov processes; Stochastic control theory; Mathematics -- Applied; Business & Economics -- Operations Research; Computers -- Programming -- Algorithms; Optimization; Operational research; Algorithms & data structures; Management science; Operations research; Mathematical optimization; Computer software; Electronic books
• Languages: English
• ISBNs: 9783319118338; 3319118331
• Related ISBNs: 9783319118321
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• 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.