Details

Autor(en) / Beteiligte

• Bensoussan, Alain
• Lions, J.-L

Titel

Applications of variational inequalities in stochastic control [electronic resource]

Link zum Volltext

• Elsevier Books AutoHoldings

Beschreibungen/Notizen

• Translation of: Applications des inéquations variationnelles en contrôle stochastique.
• Includes bibliographical references.
• Front Cover; Applications of Variational Inequalities in Stochastic Control; Copyright Page; TABLE OF CONTENTS; Chapter 1 : General introduction to optimal stopping-time problems; 1. Synopsis; 2. Fomal description of stopping time problems; 3. Analytic characterisation by dynamic programing; 4. Examples of optimal stopping-time problems; 5. Optimal stopping-time problems and free boundary problems; 6. Generalisations; 7. Various characterisations of the optimal cost function; Chapter 2 : Stochastic differential equations and linear partial differential equations of second order; Introduction
• 1. Review of the calculation of probabilities and the theory of stochastic processes2. Stochastic integrals; 3. Stochastic differential equations : strong formulation; 4. Stochastic differential equations : weak formulation; Synopsis; 5. Linear elliptic partial differential equations of second order; Synopsis; 6. Linear partial differential equations of second order, of parabolic type; Synopsis; 7. Probabilistic interpretation of the solution of boundary value problems of second order; 8. Markov process associated with the solution of a stochastic differential equation
• Chapter 3 : Optimal stopping-time problems and variational inequalitiesIntroduction; 1. Stationary variational inequalities; 2. Evolutionary variational inequalities; 3. Optimal stopping-time problems. Stationary case; 4. Optimal stopping-time problems - evolutionary case; 5. Stochastic differential games with stopping times; Synopsis; Chapter 4 : Stopping-time and stochastic optimal-control problems; Introduction; 1. Control by ""continuous variable"" and by stopping time; 2. Review material on the Hamilton-Jacobi equation; Synopsis
• 3. The Hamilton-Jacobi inequality. Operator not in divergence form4. Hamilton-Jacobi variational inequalities; 5. Optimal control and stopping times with polynomial growth; 6. The principle of separation; BIBLIOGRAPHY
• Applications of Variational Inequalities in Stochastic Control
• English