- Vaclav E. Benes
Vaclav Edvard "Vic" Benes (born 1930) is a
Czech-American mathematician, known for his contributions to the theory ofstochastic processes ,queueing theory andcontrol theory , as well as the design of telecommunicationsswitch es.He studied under
John Kemeny and gained a doctorate inmathematics atPrinceton University (1953) on a treatise on "Mathematical logic ". [ [http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=29862 Vaclav E. Benes] from the Mathematics Genealogy Project]He then worked for
Bell Labs until 1987, [ [http://cm.bell-labs.com/cm/ms/center/frmdir.html Former members of the Math Center] ] contributing toKalman filter theory [ [http://140.78.137.200/ifac50/Project_G/Control-Theory-Timeline.htm Control theory timeline] ] as well as the Beneš network, apermutation network of theClos network type. In the 1980s he held a position atColumbia University as well.Since 1987 he continued to publish independently.He was elected
IEEE Fellow (1990) for "contributions to the structure of telephone connecting networks,stochastic control , and nonlinear filtering". [ [http://www.ieee.org/web/membership/fellows/Chronology/1990.html IEEE Fellow Class of 1990] ] The "Benesfest" was celebrated atColumbia University (2000) to honor his 70th birthday. [ [http://www.cap.columbia.edu/CAP-benesfest.html Benesfest] ] He resides inMillburn, New Jersey (since 1985) where he has been a long-timemountain climber [ [http://www.research.att.com/~njas/doc/interview.html Interview] withNeil Sloane ] [ [http://www.adirondackmountainguides.com/testimonials.html Testimonial] ] member of theAmerican Alpine Club , [ [http://www.nysalpineclub.org/ New York Section of the Alpine Club] ] and currently heads the local historical society. [ [http://www.mshhistsoc.org/ Millburn - Short Hills historical society] ]Books
*"General stochastic processes in the theory of queues" (
Addison-Wesley , 1963)
*"Mathematical Theory of Connecting Networks and Telephone Traffic" (Academic Press , 1965)Journal publications
*"Mr. Mayo on “Rules” of language",
Philosophical Studies , 3(2):33-36, April 1951 (review).
*"A Partial Model for Quine's "New Foundations ", The Journal of Symbolic Logic, Vol. 19, No. 3, pp. 197-200, September 1954
*"On the Consistency of an Axiom of Enumerability", J. Symb. Log. 20(1):29-30, 1955
*"On queues with Poisson arrivals", Ann. Math. Statist., vol. 28, pp. 670–677, 1956
*"On Trunks with Negative Exponential Holding Times Serving a Renewal Process",Bell System Technical Journal , 37, pp. 211-258, 1958
*"Fluctuations of telephone traffic",Bell System Technical Journal , 38, pp. 965-974, 1959
*"Transition probabilities for telephone traffic",Bell System Technical Journal 38. pp. 211-258, 1959
*"A Sufficient Set of Statistics for a Simple Telephone Exchange Model",Bell System Technical Journal , 38, pp. 939-964, 1959
*"General Stochastic Processes in Traffic Systems with One Server",Bell System Technical Journal , 39, pp. 127-160, 1960
*"Transition Probabilities for Telephone Traffic",Bell System Technical Journal , 39, pp. 1297-1320, 1960
*"Covariance function of simple trunk group, with applications to traffic measurement",Bell System Technical Journal , 1961
*"Heuristic Remarks and Mathematical Problems Regarding the Theory of Switching Systems",Bell System Technical Journal , vol. 41, pp. 1201-1247, 1962
*"On Rearrangeable Three-Stage Connecting Networks",Bell System Technical Journal , vol. XLI, Sep. 1962, No. 5, pp. 1481-1491.
*"A "Renewal" Limit Theorem for GeneralStochastic processes ", Ann. Math. Statist. Volume 33, Number 1, 98-113, 1962
*"Growth, Complexity and Performance of Telephone Connecting Networks",Bell System Technical Journal , Vol. 62, No. 3, pp. 499-539, February 1963,
*"Optimal Rearrangeable Multistage Connecting Networks",Bell System Technical Journal , vol. 43, pp. 1641-1656, 1964
*"Permutation groups, complexes and rearrangeable connecting network",Bell System Technical Journal , 43, 4:1619-1640, 1964.
*"Index Reduction ofFM Waves by Feed-Back and Power-Law Nonlinearities",Bell Labs Technical Journal , Vol.XLIV, No.4, pp. 581-601, April 1965
*"Programming and control problems arising from optimal routing in telephone networks",SIAM Journal on Control, 4(??):6–18, 1966
*"Existence of finite invariant measures forMarkov process es", Proc. Amer.Math. Soc., 18:1058-1061, 1967.
*"On some proposed models for traffic in connecting networks",Bell Labs Technical Journal , 46:105–116, 1967
*Benes andLawrence Shepp , "Wiener Integrals Associated withDiffusion processes ",Theory of Probability , 13, pages 498-501, 1968
*"Finite Regular Invariant Measures for Feller Processes",Journal of Applied Probability , Vol. 5, No. 1, pages 203-209, April 1968
*"Existence of optimal strategies based on specified information, for a class of stochastic decision problems",SIAM Journal on Control, 8(??):179–188, 1970
*"Existence of optimal stochastic control laws",SIAM Journal on Control 9(?):446-475, 1971
*"Proving the rearrangeability of connecting networks by group calculations,",Bell Labs Technical Journal , vol.45, pp.421–434, 1975
*"Full "bang" to reduce predicted miss is optimal",SIAM Journal on Control, 15(?):52-83, 1976
*"On Kailath's innovation conjecture",Bell Labs Technical Journal 55:7, pp. 981-1001, 1976
*"Nonexistence of strong nonanticipating solutions to stochastic DEs: implications for functional DEs, filtering, and control."Stochastic Processes Applied 5:3, 243-263., 1977
*"Reduction of network states under symmetries",Bell System Technical Journal , 57(1):111–149, 1978
*Benes,Lawrence Shepp andHans S. Witsenhausen , "Some Solvable Stochastic Control Problems," Stochastics 4, 39-83, 1980
*"Least-Squares Estimator for Frequency Shift Position Modulation in White Noise", pp. 1289-1296, Sept. 1980
*René K. Boell and V. E. Benes, "Recursive non-linear estimation of a diffusion acting as the rate of an observedPoisson process ,IEEE Trans. Information Theory, vol. 26: (5), pp. 561–575, 1980.
*"Exact Finite Dimensional Filters for Certain Diffusions with Nonlinear Drift",Stochastics , 5, pp. 65-92, 1981.
*Benes andIoannis Karatzas , "Estimation and control for linear, partially observable systems with non-gaussian initial distribution", InStochastic Processes & Applications , 14, pages 233-248, 1981
*Benes and Karatzas, "On the relation ofZakai equation and Mortensen's equation",SIAM Journal on Control and Optimization, 21 pp. 472-489, 1983
*Benes and Karatzas, "Filtering of diffusions controlled through their conditional measures", Stochastics, 13, pp. 1–23, 1984
*R. A. Spanke and V. E. Benes, "N-stage planar optical permutation network",Applied Optics 26, 1226-, 1987
*"Quadratic approximation by linear systems controlled from partial observations", In Stochastic Analysis: Liber Amicorum for Moshe Zakai,Academic Press , 1991
*Benes,Kurt Helmes andRaymond. W. Rishel , "Pursuing a maneuvering target which uses a random process for its control",IEEE Trans. on Automatic Control, 40(2), 1995
*Benes andRobert J. Elliott , "Finite dimensional risk sensitive information states", I.F.A.C. Symposium on Nonlinear Control System Design, Lake Tahoe, CA, 471-476, June 1995
*Benes andRobert J. Elliott , "Finite-dimensional solutions of a modifiedZakai equation ", Mathematics of Control, Signals and Systems, 9, 341-351, 1996
*"Nonlinear filtering and optimal quality control", inJournal of Applied Mathematics and Stochastic Analysis , vol. 11, no. 3, pp. 225-230, 1998.References
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