Numerical solution of stochastic differential equations

Numerical solution of stochastic differential equations, P. E. Kioeden and E. Platen, Springer-Verlag (1992). 632 pp. $59.00 ISBN 0-386-54062-8     

Book reviews

Devroye, L.; L. Györfi: Nonparametric Density Estimation: the L1 View. John Wiley & Sons New York, Chichester, Brisbane, Toronto, Singapore 1985, XI, 356 p., £ 45.90, ISBN 0-471816469

Gericke, H.: Mathematik in Antike und Orient. Springer-Verlag Berlin, Heidelberg, New York, Tokyo 1984, 140.Abb., 4 Kartenskizzen, XII, 292 S., DNI 98,-, ISBN 3-540-11647-8

K. ITö (ed.) StochasticAnalysis. Proceedings of the Traniguchi Internationaloal Symposium on Stochastic Analysis, Katata and Kyoto, 1982. North-Holland Mathematical Library, Vol. 32, North-Holland Publishing Company, Amsterdam 1984, 488 pages, Dfl. 250.- ISBN 0-444-87588-3

Weizenbaum, J.: Die Macht der Computer und dic Ohnmaeht der Vernuutt, Suhrkamp Taschenbuch Wissenschaf't 274. Suhrkamp Verlag Frankfurt/M. 1978, 368 S., DM 16,-, ISBN 3-518-27874-6

Krylov, N.V.; R. Sh. Lipiser; A.A Novikov (eds.): Statistics and Control of Stochastic Processes. Steklov Seminar, 1984. Springer-Verlag Berlin, Heidelberg, New York, Tokyo 1985, XIII, 507 S., DM 198, -, ISBN 3.540-96101-1

Sachs, H. (ed.): Graphs, Hypergraphs and Applications. Proceedings of the Conference on Graph Theory held in Eyba, Oct. 1984.. 'I'eubner-Texte zur Mathematik 73 Teubner Verlagsgesellschaft Leipzig 1985, 224 S., 23,-M, ISBN 666275-5

Bhat, U. Narayan; Elements of Applied Stochastic Processes. 2. Ed. Jonoh Wilet & Sons New York, Chichester, Brisbane, Toronto, Singapore 1984, IX, 685 p., £ 52.00, ISBN 0-471-87826-X

Methods of Operations Research. Bd, 66. Verlag Anton Hain Meisenheim, Königstein 1985, 410 S., DM 120,-, ISBN 3..445..02400..6

Maier, T.: Intervall-Input-Ontput-Rechnung. Mathernat.ical Systems in Economics. 101. Verlag Anton Rain, Meisenheim GmbH InigiteinTs. 1985, X, 338 S., DM 72,-, ISBN 3-445-02399-9.

Sawaragi, Y.; H. Nakayama; T. Tanino: Theory of Multi-objective Optimization. Mathematics in Science and Engineering. 176. Academic Press Orlando, San Diego, New York, London, Toronto 1985, 320 pp., $ 48.00, ISBN 0-12-620370-9.

Krämer, W.: Trend in ökonometrischen Modellen. Mathematical Systems in Economics. 93. Athenaum/Hain Konigstein 1985, 172 S., DM 48,-, ISBN 3-445-02386-7.     

Book reviews

Desch, W.; F. Kappel; K. Kunisch: Estimation and Control of Distributed Parameter Systems. International Series of Numerical Mathematics. Vol. 100. Birkhauser Verlag AG Base1 1991, 396pp., DM 138, ISBN 3-7643-2676-X.

Klein, D. J.; M. RandiC: Mathematical Chemistry. Proceedings of the 3rd International Conference on Mathematical Chemistry, Galveston (USA) March 1989. VCH Weinheim 1990, 416pp., 59 fig., DM265,ISBN 3-527-28240-0.

Mezey, P. C.: Mathematical Modeling in Chemistry. VCH Weinheim 1991,416 pp., DM 265,ISBN 3-527-28292-0.

Lewandowski, A.; V. Volkovich (eds.): Multiobjective Problems of Mathematical Programming. Proceedings Yalta, USSR 1988. Lecture Notes in Economics and Mathematical Systems, Vol. 351. Springer-Verlag Berlin, Heidelberg, New York, London 1991, VII, 314 pp., Softcover, DM 61,- ISBN 3-540-532-6

Guddat, J.; F. Guerra Vasquez; H. Th. Jongen: Parametric Optimization: Singularities, Pathfollowing and Jumps. John Wiley & Sons Ltd. Baffins Lane, Chichester 1990, 216 pp., $80.40, ISBN 0-471-92807-0.

van der Geer, G.; F. Oort; J. Steenbrink (eds.): Arithmetic Algebraic Geometry. Progress in Mathematics, Vol. 89. Birkhauser Verlag Basel, Boston, Berlin l991, 446 pp., SFr. 78.-, ISBN 3-7643-3513-0.

Solomon, A.: PC Viruses-Detection, Analysis and Cure. Springer Verlag Berlin, Heidelberg, New York, Paris, London 1991, IX, 288 pp., DM 74,ISBN 3-540-19691-9.     

How to Choose Winning Lottery Numbers—Secret Ways to Win Big Money

Abstract

The New Bookstore in Town—Books Found on the Shelf

Reasoning with Statistics, Third ed. by Frederick Williams. New York: Holt, Reinhart and Winston, 1986, 224 pp., $16.95, paperback (ISBN 0-03-019536-5). Reviewed by Michael M. Meyer

Envisioning Information by Edward R. Tufte, Cheshire, Connecticut: Graphics Press, 1990, 126 pp., $48., hardcover (ISBN 0-961-3921-1-8). Reviewed by William F. Eddy     

Book reviews

Bauer, H., Maßund Integrationstheorie. De Gruyter Lehrbuch, Walter de Gruyter & Co., Berlin, New York, 1990, XVIII, 259 pp, DM 78, —, ISBN 3-11-012773-3 GB, DM 42, —, (ISBN 3-11-012772-5 KT).

?inlar, E. (ed.), Fitzsimmons, P. J., Williams, R. J. (managing eds.), Seminar on Stochastic Processes, 1990. Progress in Probability, Vol. 24, Birkhaüser Boston, Basel, Berlin 1991, VIII + 351 pp., DM 38,—, ISBN 0-8176-3488-6.

Spalt, D. D. (ed.). Rechnen mit dem Unendlichen. Beiträ zur Entwicklung der Nichtstandard Gegenstandes Birkhaüser Verlag Basel, Boston, Berlin, 1990, 243 pp. DM 49.80, ISBN 3-7643-2568-3.     

On the path regularity of a stochastic process in a hilbert space,defined by the ito integral

Poisson Processes, by J.F.C. Kingman. Clarendon Press (Oxford University Press), Oxford (1993), 104 pp. $ 39,95 ISBN 0-19-853693-3     

Project scheduling: a review of recent books

This paper is a review of three related books:Erik L. Demeulemeester and Willy S. Herroelen, Project Scheduling, A Research Handbook, Kluwer, 2002, ISBN 1-4020-7051-9, 708 pp., $185, €202.Ulrich Dorndorf, Project Scheduling with Time Windows—From Theory to Applications, Springer, 2002, ISBN 3-7908-1516-0, 175 pp., €37.95.Klaus Neumann, Christoph Schwindt and Jürgen Zimmermann, Project Scheduling with Time Windows and Scarce Resources—Temporal and Resource-Constrained Project Scheduling with Regular and Nonregular Objective Functions, Springer, 2003, ISBN 3-540-40125-3, 398 pp., $ 84.95, €49.95.     

Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.     

Stochastic flows and stochastic differential equations

Stochastic flows and stochastic differential equations by H. Kunita, Department of Applied Science, Kyushu University, Cambridge University Press, Cambridge, November 1990, 346 pp. ISBN 0 521 35050 6     

Homeomorphic property of solutions of SDE driven by countably many Brownian motions with non-Lipschitzian coefficients

We study m-dimensional SDE , where {Wi}_i?1 is an infinite sequence of independent standard d-dimensional Brownian motions. The existence and pathwise uniqueness of strong solutions to the SDE was established recently in [Z. Liang, Stochastic differential equations driven by countably many Brownian motions with non-Lipschitzian coefficients, Preprint, 2004]. We will show that the unique strong solution produces a stochastic flow of homeomorphisms if the modulus of continuity of coefficients is less than , ?∈[0,1) with ?(−1)=1, and the coefficients are compactly supported.     

Book Reviews

Abstract

The Mathematical and Computational Sciences in Emerging Manufacturing Technologies and Management Practices by Avner Friedman, James Glimm, and John Lavery. Philadelphia: Society of Industrial and Applied Mathematics, 1992, 86 pp., free (ISBN 0-89871-307-2). Reviewed by Michael M. Meyer

The Physics of Chance by Charles Ruhla. Oxford, U.K.: Oxford University Press, 1992, 222 pp., $55 (hardcover), $27.95 (paperback) (ISBN 0-19-853960-6). Translated by G. Barton. Reviewed by Michael M. Meyer

The Future of the Survey of Income and Program Participation edited by Constance F. Citro and Graham Kalton. Washington, DC: National Academy Press, 1993, 284 pp. Reviewed by Michael M. Meyer     

Book reviews

d'Alessandro, P., A Conical Approach to Linear Programming Scalar and Vector Optimization Problems, Gordon and Breach Science Publishers, Australia Canada China France Germany India Japan Luxembourg Malaysia The Netherlands Russia Singapore Switzerland Thailand United Kingdom 1997, 312 pp., ISBN 90- 5699-031-4.

Fang, S.-C., Rajasekera, J. R. and Tsao, H. S. J., Entropy Optimization and Mathematical Programming, Kluwer's International Series. Kluwer Academic Publishers, Boston London Dordrecht, 1997, pp. 343, US $120.00; ISBN 0-7923-9939-0.

Golshtein, E. G. and Tretyakov, N. V., Modified Lagrangians Monotone Maps in Optimization, John Wiley & Sons, New York Chicester Brisbane Toronto Singapore 1996,438 pp., £55.00, ISBN 0-471-54821-9.

Hoffmann, K.-H., Leugering, G. and Troltzsch, F. (Eds.), Optimal Control of Partial Differential Equations, International Confa-ence in Chemnitz, Germany, April 20-25, 1998; International Series of Numerical Mathematics ISNM, Vol. 133, Birkhauser Verlag AG, Basel*Boston-Berlin 1999, viii+323 pp., DM 188.00, ISBN 3-7643- 6151-4.     

International Encyclopedia of the Social Sciences,Quotations, Volume 19

Abstract

The Drummer Was the First to Die by Liza Pennywitt Taylor. New York: St. Martin's Press, 1992, 309 pp., $19.95 hardcover. Reviewed by Sally C. Morton

Rubbish! The Archaeology of Garbage by William Rathje and Cullen Murphy. New York: HarperCollins, 1992, 250 pp., $23.00 (ISBN 0-06-016603-7). Reviewed by Stephen E. Fienberg     

Controlled markov processes and viscosity solutions

Controlled markov processes and viscosity solutions by W. H. Fleming and H. M. Soner. Springer-Verlag, New York (1993), 428 pp., $ 49.95. ISBN 0-387-97927-1.     

Book Reviews

Abstract

Housing America in the 1980s by John S. Adams. New York: The Russell Sage Foundation, 1988, 352 pp., $65 hardcover (ISBN 0-97154-003-7). Reviewed by Michael M. Meyer     

Itô’s stochastic calculus and Heisenberg commutation relations

Stochastic calculus and stochastic differential equations for Brownian motion were introduced by K. Itô in order to give a pathwise construction of diffusion processes. This calculus has deep connections with objects such as the Fock space and the Heisenberg canonical commutation relations, which have a central role in quantum physics. We review these connections, and give a brief introduction to the noncommutative extension of Itô’s stochastic integration due to Hudson and Parthasarathy. Then we apply this scheme to show how finite Markov chains can be constructed by solving stochastic differential equations, similar to diffusion equations, on the Fock space.     

BOOK REVIEW

LARGE MARINE ECOSYSTEMS: PATTERNS, PROCESSES AND YIELDS, K. Sherman, L.M. Alexander, and B.D. Gold, AAAS, 1991, 247 pp., soft cover, ISBN 0-87168-348-9, $34.95, $27.95 members     

Statistical Whigmaleeries

Abstract

An Introduction to Regression Graphics by R. Dennis Cook and Sanford Weisberg New York: John Wiley, 1994, xiii + 253 pp., 2 disks. Hardcover: US $54.95, ISBN 0-471-00839-7. Reviewed by John D. Fox     

Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients

We prove a general theorem that the -valued solution of an infinite horizon backward doubly stochastic differential equation, if exists, gives the stationary solution of the corresponding stochastic partial differential equation. We prove the existence and uniqueness of the -valued solutions for backward doubly stochastic differential equations on finite and infinite horizon with linear growth without assuming Lipschitz conditions, but under the monotonicity condition. Therefore the solution of finite horizon problem gives the solution of the initial value problem of the corresponding stochastic partial differential equations, and the solution of the infinite horizon problem gives the stationary solution of the SPDEs according to our general result.     

Large deviations for stochastic partial differential equations driven by a Poisson random measure

Stochastic partial differential equations driven by Poisson random measures (PRMs) have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential equation (PDE). A systematic framework for the study of probabilities of deviations of the stochastic PDE from the deterministic PDE is through the theory of large deviations. The goal of this work is to develop the large deviation theory for small Poisson noise perturbations of a general class of deterministic infinite dimensional models. Although the analogous questions for finite dimensional systems have been well studied, there are currently no general results in the infinite dimensional setting. This is in part due to the fact that in this setting solutions may have little spatial regularity, and thus classical approximation methods for large deviation analysis become intractable. The approach taken here, which is based on a variational representation for nonnegative functionals of general PRMs, reduces the proof of the large deviation principle to establishing basic qualitative properties for controlled analogues of the underlying stochastic system. As an illustration of the general theory, we consider a particular system that models the spread of a pollutant in a waterway.