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The Fokker-Planck equation : methods of solution and applications
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ISBN: 354061530X 3642615449 9783540615309 Year: 1989 Volume: 18 Publisher: New York : Springer-Verlag,

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Stochastic differential equations and applications
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ISBN: 0122682025 0122682017 1322557373 1483217876 1322557381 1483217884 9780122682018 Year: 1975 Volume: 28 Publisher: New York : Academic Press,


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Stochastic differential equations : theory and applications
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ISBN: 0471033596 9780471033592 Year: 1974 Publisher: New York London Sidney : J. Wiley,


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Stochastic control and mathematical modeling
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ISBN: 9780521195034 0521195039 9781139087353 9781107086975 1107086973 1139087355 9781107093195 1107093198 1139885812 1107101875 1107099374 1107090032 1306148359 Year: 2010 Volume: 131 Publisher: Cambridge New York

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This is a concise and elementary introduction to stochastic control and mathematical modelling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Contents include the basics of analysis and probability, the theory of stochastic differential equations, variational problems, problems in optimal consumption and in optimal stopping, optimal pollution control, and solving the Hamilton-Jacobi-Bellman (HJB) equation with boundary conditions. Major mathematical prerequisites are contained in the preliminary chapters or in the appendix so that readers can proceed without referring to other materials.

Stochastic integration and differential equations: a new approach
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ISBN: 3540003134 3642055605 3662100614 9783540003137 Year: 2005 Volume: 21 Publisher: Berlin Springer

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It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emeryâ¬(tm)s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.

Stochastic differential equations : an introduction with applications
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ISBN: 3540047581 9783540047582 3642143946 9783642143946 Year: 2007 Publisher: Berlin : Springer,

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Keywords

Stochastic differential equations. --- 519.216 --- 517.9 --- Stochastic differential equations --- 681.3*H35 --- 681.3*H1 --- 681.3*H1 Models and principles (Information systems) --- Models and principles (Information systems) --- 681.3*H35 On-line information services: data bank sharing --- On-line information services: data bank sharing --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- 519.2 --- Differential equations --- Fokker-Planck equation --- Mathematical analysis. --- Analysis (Mathematics). --- Probabilities. --- Mathematical physics. --- System theory. --- Calculus of variations. --- Partial differential equations. --- Analysis. --- Probability Theory and Stochastic Processes. --- Theoretical, Mathematical and Computational Physics. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Partial Differential Equations. --- Partial differential equations --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Systems, Theory of --- Systems science --- Science --- Physical mathematics --- Physics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- 517.1 Mathematical analysis --- Mathematical analysis --- Philosophy --- Physics. --- Mathematics. --- System theory --- Math --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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