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Produktbild: Numerical Methods For Stochast
Band 24

Numerical Methods For Stochast

Aus der Reihe Stochastic Modelling and Appli

Fr. 198.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.07.2012

Verlag

Springer

Seitenzahl

439

Maße (L/B/H)

23.4/15.6/2.3 cm

Gewicht

626 g

Auflage

Softcover reprint of the original 1st ed. 1992

Sprache

Englisch

ISBN

978-1-4684-0443-2

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

01.07.2012

Verlag

Springer

Seitenzahl

439

Maße (L/B/H)

23.4/15.6/2.3 cm

Gewicht

626 g

Auflage

Softcover reprint of the original 1st ed. 1992

Sprache

Englisch

ISBN

978-1-4684-0443-2

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  • Produktbild: Numerical Methods For Stochast
  • 1 Review of Continuous Time Models.- 1.1 Martingales and Martingale Inequalities.- 1.2 Stochastic Integration.- 1.3 Stochastic Differential Equations: Diffusions.- 1.4 Reflected Diffusions.- 1.5 Processes with Jumps.- 2 Controlled Markov Chains.- 2.1 Recursive Equations for the Cost.- 2.2 Optimal Stopping Problems.- 2.3 Discounted Cost.- 2.4 Control to a Target Set and Contraction Mappings.- 2.5 Finite Time Control Problems.- 3 Dynamic Programming Equations.- 3.1 Functionals of Uncontrolled Processes.- 3.2 The Optimal Stopping Problem.- 3.3 Control Until a Target Set Is Reached.- 3.4 A Discounted Problem with a Target Set and Reflection.- 3.5 Average Cost Per Unit Time.- 4 The Markov Chain Approximation Method: Introduction.- 4.1 The Markov Chain Approximation Method.- 4.2 Continuous Time Interpolation and Approximating Cost Function.- 4.3 A Continuous Time Markov Chain Interpolation.- 4.4 A Random Walk Approximation to the Wiener Process.- 4.5 A Deterministic Discounted Problem.- 4.6 Deterministic Relaxed Controls.- 5 Construction of the Approximating Markov Chain.- 5.1 Finite Difference Type Approximations: One Dimensional Examples.- 5.2 Numerical Simplifications and Alternatives for Example 4.- 5.3 The General Finite Difference Method.- 5.4 A Direct Construction of the Approximating Markov Chain.- 5.5 Variable Grids.- 5.6 Jump Diffusion Processes.- 5.7 Approximations for Reflecting Boundaries.- 5.8 Dynamic Programming Equations.- 6 Computational Methods for Controlled Markov Chains.- 6.1 The Problem Formulation.- 6.2 Classical Iterative Methods: Approximation in Policy and Value Space.- 6.3 Error Bounds for Discounted Problems.- 6.4 Accelerated Jacobi and Gauss-Seidel Methods.- 6.5 Domain Decomposition and Implementation on Parallel Processors.- 6.6 A State Aggregation Method.- 6.7 Coarse Grid-Fine Grid Solutions.- 6.8 A Multigrid Method.- 6.9 Linear Programming Formulations and Constraints.- 7 The Ergodic Cost Problem: Formulations and Algorithms.- 7.1 The Control Problem for the Markov Chain: Formulation.- 7.2 A Jacobi Type Iteration.- 7.3 Approximation in Policy Space.- 7.4 Numerical Methods for the Solution of (3.4).- 7.5 The Control Problem for the Approximating Markov Chain.- 7.6 The Continuous Parameter Markov Chain Interpolation.- 7.7 Computations for the Approximating Markov Chain.- 7.8 Boundary Costs and Controls.- 8 Heavy Traffic and Singular Control Problems: Examples and Markov Chain Approximations.- 8.1 Motivating Examples.- 8.2 The Heavy Traffic Problem: A Markov Chain Approximation.- 8.3 Singular Control: A Markov Chain Approximation.- 9 Weak Convergence and the Characterization of Processes.- 9.1 Weak Convergence.- 9.2 Criteria for Tightness in Dk [0, ?).- 9.3 Characterization of Processes.- 9.4 An Example.- 9.5 Relaxed Controls.- 10 Convergence Proofs.- 10.1 Limit Theorems and Approximations of Relaxed Controls.- 10.2 Existence of an Optimal Control: Absorbing Boundary.- 10.3 Approximating the Optimal Control.- 10.4 The Approximating Markov Chain: Weak Convergence.- 10.5 Convergence of the Costs: Discounted Cost and Absorbing Boundary.- 10.6 The Optimal Stopping Problem.- 11 Convergence for Reflecting Boundaries, Singular Control and Ergodic Cost Problems.- 11.1 The Reflecting Boundary Problem.- 11.2 The Singular Control Problem.- 11.3 The Ergodic Cost Problem.- 12 Finite Time Problems and Nonlinear Filtering.- 12.1 The Explicit Approximation Method: An Example.- 12.2 The General Explicit Approximation Method.- 12.3 The Implicit Approximation Method: An Example.- 12.4 The General Implicit Approximation Method.- 12.5 The Optimal Control Problem: Approximations and Dynamic Programming Equations.- 12.6 Methods of Solution, Decomposition and Convergence.- 12.7 Nonlinear Filtering.- 13 Problems from the Calculus of Variations.- 13.1 Problems of Interest.- 13.2 Numerical Schemes and Convergence for the Finite Time Problem.- 13.3 Problems with a Controlled Stopping Time.- 13.4 Problems with a Discontinuous Running Cost.- 14 The Viscosity Solution Approach to Proving Convergence of Numerical Schemes.- 14.1 Definitions and Some Properties of Viscosity Solutions.- 14.2 Numerical Schemes.- 14.3 Proof of Convergence.- References.- List of Symbols.