Stochastic Control of Hereditary Systems and Applications
ThisresearchmonographdevelopstheHamilton-Jacobi-Bellman(HJB)theory viathedynamicprogrammingprincipleforaclassofoptimalcontrolproblems for shastic hereditary differential equations (SHDEs) driven by a standard Brownian motion and with a bounded or an unbounded but fading m- ory. These equations represent a class of inflnite-dimensional shastic systems that become increasingly important and have wide range of applications in physics, chemistry, biology, engineering, and economics/?nance. The wide applicability of these systems is due to the fact that the reaction of re- world systems to exogenous effects/signals is never “instantaneous” and it needs some time, time that can be translated into a mathematical language by some delay terms. Therefore, to describe these delayed effects, the drift and diffusion coeficients of these shastic equations depend not only on the current state but also explicitly on the past history of the state variable. The theory developed herein extends the finite-dimensional HJB theory of controlled diffusion processes to its inflnite-dimensional counterpart for c- trolledSHDEsinwhichacertaininflnite-dimensionalBanachspaceorHilbert space is critically involved in order to account for the bounded or unbounded memory. Another type of inflnite-dimensional HJB theory that is not treated in this monograph but arises from real-world application problems can often be modeled by controlled shastic partial differential equations. Although they are both inflnite dimensional in nature and are both in the infancy of their developments, the SHDE exhibits many characteristics that are not in common with shastic partial differential equations. Consequently, the HJB theory for controlled SHDEs is parallel to and cannot betreated as a subset of the theory developed for controlled shastic partial differential equations.
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Stochastic Control of Hereditary Systems and Applications
ThisresearchmonographdevelopstheHamilton-Jacobi-Bellman(HJB)theory viathedynamicprogrammingprincipleforaclassofoptimalcontrolproblems for shastic hereditary differential equations (SHDEs) driven by a standard Brownian motion and with a bounded or an unbounded but fading m- ory. These equations represent a class of inflnite-dimensional shastic systems that become increasingly important and have wide range of applications in physics, chemistry, biology, engineering, and economics/?nance. The wide applicability of these systems is due to the fact that the reaction of re- world systems to exogenous effects/signals is never “instantaneous” and it needs some time, time that can be translated into a mathematical language by some delay terms. Therefore, to describe these delayed effects, the drift and diffusion coeficients of these shastic equations depend not only on the current state but also explicitly on the past history of the state variable. The theory developed herein extends the finite-dimensional HJB theory of controlled diffusion processes to its inflnite-dimensional counterpart for c- trolledSHDEsinwhichacertaininflnite-dimensionalBanachspaceorHilbert space is critically involved in order to account for the bounded or unbounded memory. Another type of inflnite-dimensional HJB theory that is not treated in this monograph but arises from real-world application problems can often be modeled by controlled shastic partial differential equations. Although they are both inflnite dimensional in nature and are both in the infancy of their developments, the SHDE exhibits many characteristics that are not in common with shastic partial differential equations. Consequently, the HJB theory for controlled SHDEs is parallel to and cannot betreated as a subset of the theory developed for controlled shastic partial differential equations.
109.99
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Stochastic Control of Hereditary Systems and Applications
406
Stochastic Control of Hereditary Systems and Applications
406
109.99
In Stock
Product Details
| ISBN-13: | 9780387758053 |
|---|---|
| Publisher: | Springer New York |
| Publication date: | 01/23/2008 |
| Series: | Stochastic Modelling and Applied Probability , #59 |
| Edition description: | 2008 |
| Pages: | 406 |
| Product dimensions: | 6.10(w) x 9.25(h) x 0.04(d) |
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