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Author: Jürgen Groh
Publisher:
ISBN:
Category : Diffusion processes
Languages : de
Pages : 42
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Author: Jürgen Groh
Publisher:
ISBN:
Category : Diffusion processes
Languages : de
Pages : 42
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Author: Diane Sheng
Publisher:
ISBN:
Category :
Languages : en
Pages : 134
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Book Description
We consider a class of problems in the optimal control of one-dimensional diffusion processes, with the objective to minimize expected discounted cost over an infinite planning horizon. There are available a finite number of control modes (actions), and the state of the system changes locally like a Brownian Motion whose drift and variance depend upon the control mode being employed (but not upon the current state). There is a holding cost which is proportional to the state of the system and is independent of the control mode. In addition to these continuous costs, there are lump costs associated with a change in action. The state space may be either a finite or semi-infinite interval, and different types of boundary behavior are considered. Absorbing barriers arise in applications to collective risk and insurance, while reflecting barriers are natural for problems in the optimal control of queueing and storage systems. When there are only two control modes, one expects an optimal policy characterized by a pair of critical numbers. For various special cases, it is shown that such an optimal policy exists, and (complicated) formulas for the critical numbers are derived. (Author).
Author: Vivek S. Borkar
Publisher: Longman
ISBN:
Category : Control theory
Languages : en
Pages : 212
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Author: Martin Lee Puterman
Publisher:
ISBN:
Category : Control theory
Languages : en
Pages : 100
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The author considers three problems in the optimal control of diffusion processes. The first is that of optimally controlling a diffusion process on a compact interval. The second problem is that of optimally controlling a diffusion process on a bounded subset of Euclidean n-space, with refledtion on the boundary. The last problem arises in controlling a continuous time production process. (Author).
Author:
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 562
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Author: Stanley Roy Pliska
Publisher:
ISBN:
Category : Control theory
Languages : en
Pages : 122
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The paper is concerned with the optimal control of a one-dimensional stationary diffusion process on a compact interval. The drift and diffusion coefficients depend upon a stationary control assumed to be a piece-wise continuous function of the state. The costs generated by the process are functions of both the control and the sample path of the process. Mandl's concept of a controlled diffusion process is generalized by allowing the controls to be vector-valued with the set of admissible control actions defined by a piecewise continuous set-valued function on the state space. Both single and multi-person problems are considered. The main results include necessary and sufficient conditions for a control to be 'optimal' and conditions assuring the existence of a piecewise continuous optimal control. Applications are given to problems of controlling reservoirs, pollution, queues, investments, welfare, and warfare.
Author: Nikolaĭ Vladimirovich Krylov
Publisher:
ISBN:
Category : Control theory
Languages : en
Pages : 328
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Author: Gary Catterton Myers
Publisher:
ISBN:
Category : Diffusion processes
Languages : en
Pages : 260
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Author:
Publisher:
ISBN:
Category : Stochastic integral equations
Languages : en
Pages : 356
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Author: Jerome Barry Shapiro
Publisher:
ISBN:
Category :
Languages : en
Pages :
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