Бенеш, Вацлав Эдвард

Бенеш учился у Джона Джорджа Кемени и получил степень доктора технических наук в Принстонском университете в 1953 году по теме «Математическая логика»[1].

Затем, до 1987 года, он работал в Лабораториях Белла[2] по теории Калмановских фильтров[3], а также в области перестановочных сетей Клоза и им подобных. Кроме того, в 1980-х годах он занимал должность в Колумбийском университете. С 1987 года публикуется как независимый автор.

В 1990 году Бенеш был избран членом общества IEEE за вклад в изучение структур телефонных коммутационных (соединительных) сетей, стохастического управления и нелинейной фильтрации[4]. В честь 70-летия учёного в Колумбийском университете праздновался «Бенешфест». Работы учёного были востребованы, в частности, при разработке коммутационных полей для систем быстрой коммутации пакетов[5] и, соответственно, ATM.

С 1985 года Бенеш живёт в Миллбёрне, штат Нью-Джерси, США, где в течение долгих лет он занимался альпинизмом[6][7], является членом Американского клуба альпинистов (American Alpine Club)[8], и в настоящее время возглавляет местное историческое общество[9]. Его жена Дженет Франклин — племянница Норберта Винера.

• Vaclav E. Benes,. General stochastic processes in the theory of queues. — Addison-Wesley Pub. Co., 1963. — С. 88.

• Vaclav E. Benes,. Mathematical Theory of Connecting Networks and Telephone Traffic. — Academic Press, 1965.

• В. Э. Бенеш. Математические основы теории телефонных сообщений = Mathematical theory of connecting networks and telephone traffic / И. Н. Коваленко (ред.), В. И. Нейман, А. Д. Харкевич (пер.). — М.: Связь, 1968. — 292 с. — 6,000 экз.

• Bernard Mayo on “Rules” of language, Philosophical Studies, 3(2):33–36, April 1951 (review).
• A Partial Model for Willard Van Orman Quine "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 General Stochastic 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 of Frequency Modulation (FM) 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, Society for Industrial and Applied Mathematics (SIAM) Journal on Control, 4(??):6–18, 1966
• Existence of finite invariant measures for Markov processes, Proc. Amer.Math. Soc., 18:1058–1061, 1967.
• On some proposed models for traffic in connecting networks, Bell System Technical Journal, 46:105–116, 1967
• Benes and Lawrence Shepp, Wiener Integrals Associated with Diffusion processes, Theory of Probability, 13, pages 498–501, 1968
• Finite Regular Invariant Measures for William 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, Society for Industrial and Applied Mathematics (SIAM) Journal on Control, 8(??):179–188, 1970
• Existence of optimal stochastic control laws, Society for Industrial and Applied Mathematics (SIAM) Journal on Control 9(?):446–475, 1971
• Applications of group theory to connecting networks, Bell System Technical Journal, vol.45, pp. 407–420, 1975
• Proving the rearrangeability of connecting networks by group calculations, Bell System Technical Journal, vol.45, pp. 421–434, 1975
• Full "bang" to reduce predicted miss is optimal, Society for Industrial and Applied Mathematics (SIAM) Journal on Control, 15(?):52–83, 1976
• On Thomas Kailath innovation conjecture, Bell System 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 and Hans 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 observed Poisson 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 and Ioannis Karatzas, Estimation and control for linear, partially observable systems with non-gaussian initial distribution, In Stochastic Processes & Applications, 14, pages 233–248, 1981
• Benes and Karatzas, On the relation of Zakai equation and Mortensen's equation, Society for Industrial and Applied Mathematics (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 and Raymond. W. Rishel, Pursuing a maneuvering target which uses a random process for its control, IEEE Trans. on Automatic Control, 40(2), 1995
• Benes and Robert 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 and Robert J. Elliott, Finite-dimensional solutions of a modified Zakai equation, Mathematics of Control, Signals, and Systems, 9, 341–351, 1996
• Nonlinear filtering and optimal quality control, in Journal of Applied Mathematics and Stochastic Analysis, vol. 11, no. 3, pp. 225–230, 1998.