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Full list of Publications

See publications selected by topics and selected downloadable [ ] publications in [ Research Interests].

I. BOOKS
1a. Sequential Control with Incomplete Information (with E.L. Presman), 1982, Science, Moscow (in Russian).
1b. Sequential control with incomplete information. The Bayesian approach to multi-armed bandit problems, (with E.L. Presman). Translated from the 1982 Russian original, edited and with a preface by E. A. Medova-Dempster and M. A. H. Dempster. Economic Theory, Econometrics, and Mathematical Economics. Academic Press, Inc., San Diego, CA, 1990. xxviii+266 pp. ISBN: 0-12-564435-3

II. PAPERS
List of Publications on Math Sci Net. (A1, A2,...)

Publications which are not yet included in Math Sci Net., published in economic journals, in collections of papers, in publications of CEMI, in Russian and so on.

B1 On a class of degenerative diffusion processes. Theory Probability Appl. 12 (1967), 490--496.
B2 On uniqueness classes for degenerating parabolic equations. Mathematics of the USSR - Sbornik, 14 (1971), 453--469.
B3 The best choice problem for a random number of objects. (with E.L. Presman). Theory Probability Appl. 17 (1972), 657--668.
B4 The points of equilibrium in the generalized game best choice problem. (with E.L. Presman). Theory Probability Appl. 20 (1975), 770--781.
B5 The game settings in the best choice problem. Cybernetics, 2, (1976), 70-75.
B6 The stochastic models of economical dynamics with R&D. (with V.I. Arkin and E.L.Presman), In: Studies on Modelling of R&D and Control of Economic Processes, Central Econom. Math. Inst. Press, Moscow, 1976, 56--106, (in Russian).
B7 A model of resource allocation under incomplete information. In: Studies on Modelling R&D and Control of Economic Processes, Central Econom. Math. Inst. Press, Moscow, 1976, 161--201, (in Russian).
B8 The game setting of optimal stopping. The existence and uniqueness of equilibrium points. (with E.L. Presman), In: Stochastic Control Problems in Economics, Moscow, Science, 1977, 123--148, (in Russian).
B9 The choice of decision moments in game setting. (with E.L. Presman), In: Stochastic Control Problems in Economics, Science, Moscow, 1977, 149-184 (in Russian).
B10 The two-armed bandit problems in continuous time. (with E.L. Presman), In: Stochastic Processes and Control, Science, Moscow, 1978, 154--204, (in Russian).
B11 The asymptotic behavior of value functions in the two-armed bandit problems. (with E. L. Presman), In: Stochastic Models and Control of Economic Processes, Econom. Math. Inst. Press, Moscow, 1978, 142--168, (in Russian).
B12 The asymptotic behavior of value functions in the many-armed bandit problems. (with E.L. Presman), In: Stochastic Methods in the Problems of Control of Economic Processes, Central Econom. Math. Inst. Press, Moscow, 1979, 97--132, (in Russian).
B13 The estimation of an annual profit in stochastic setting. (with G.V. Pristavko). In: Stochastic Methods in the Problems of Control of Economic Processes, Central Econom. Math. Inst. Press, Moscow, 1979, 145--162, (in Russian).
B14 On a problem of stochastic control with incomplete data. In: Stochastic Models and Control, Central Econom. Math. Inst. Press, Moscow, 1980, 185--198, (in Russian).
B15 The models of optimal control of a set of multistage programs under uncertainty. (with G.V. Pristavko). In: Stochastic Models and Control, Central Econom. Math. Press, Moscow, 1980, 105--150, (in Russian).
B16 The research and development on the competition base. (with L.L. Veger, A.D. Vainstein, and G.V. Pristavko), Notices of the Academy of Sci. of the USSR Ser. Economics, 1981, no. 2, 215--220, (in Russian).
B17 The economic effect under uncertainty. (with G.V. Pristavko). In: The Economic theory of R&D, Science, Moscow, 1982, 121-156, (in Russian).
B18 The existence of uniformly nearly optimal Markov strategies in controllable countable state chains. In: Models and Methods of Stochastic Optimization, Central Econom. Math. Inst. Press, Moscow, 1983, 213--232, (in Russian).
B19 Stationary strategies in dynamic programming with a countable state space. (with E.A. Feinberg). In: Studies on Math Econom. and Control Theory, Central Econom. Math. Inst. Press, Moscow, 1983, 137--172, (in Russian).
B20 On the relation of reliability of equipment and its period of work. (with I.A. Aliev). Econom. and Math. Methods, 20,1984, 352--355, (in Russian).
B21 Incomplete information in mechanisms of control of economics. (with V.I. Arkin, N.J. Petrakov, and others). In: The Modelling of Control Processes in Economics, Science, Moscow, 1984, 167--318, (in Russian).
B22 The models of project selection under self-financing and indexes of effectiveness. (with V.A. Tsarkov). In: Studies on Stochastic Optimization and Mathematical Economics, Central Econom. Math. Inst. Press, Moscow, 1986, 175--196, (in Russian).
B23 Stochastic model of management of parallel multistage programs. (with G.V. Pristavko). Econom. and Math. Methods, 23,1987, 677--686, (in Russian). ( Matekon XXIV, Summer 1988, 72-90).
B24 A model of program selection under presence of common blocks. (with P.K. Katyshev). In: Mathematical Models of Control under Uncertainty, Central Econom. Math. Inst. Press, Moscow, 1987, 49--78, (in Russian).
B25 The estimation of annual economic effect in deterministic and stochastic cases (with G.V. Pristavko). Econom. and Math. Methods,24,1988, 155--166, (in Russian).
B26 A model of R&D program design in the presence of common blocks (with P.K. Katyshev). In: Probability and Mathematical Economics, Central Econom. Math. Inst. Press, Moscow, 1988, 83--108, (in Russian).
B27 The asymptotic behavior of nonhomogeneous Markov chains and redistribution of incomes. In: Probability and Mathematical Economics, Central Econom. Math. Inst. Press, Moscow, 1988, 171--182, (in Russian).
B28 The allocation of expenditures between projects on realization of common blocks (with P.K. Katyshev). In: Studies on Mathematical Economics. Central Econom. Math. Insti., Moscow, 1991, (in Russian).
B29 Growth rate, internal rates of return and turnpikes in an investment model, Economic Theory, 5, 1995, 383--400.
B30 The "Join the Club'' interpretation of some graph algorithms (with H. Reiter), College Math. Journal, 27,1996, 54--58. Also translated into Russian and published in Mathematical Education, 3 , (1999), 208-212.
B31 Computational properties of algorithm ``REFUND'' for the fundamental/group inverse matrix of a Markov chain. (with J. Thornton), Proc. of the Third Int. Conf. on the Numerical Solution of Markov Chains, Saragoza, PUZ, Spain, 1999, 131--148.
B32 The state reduction and related algorithms and their applications to the study of Markov chains, graph theory, and the optimal stopping problem. Adv. Math. 145 (1999), no. 2, 159--188.
B33 Recursive Algorithm for the Fundamental/Group Inverse Matrix of a Markov Chain from an Explicit Formula, (with J. Thornton), SIAM J. on Matrix Analysis and Appl.,v. 23, #1, pp.209-224, 2001.
B34 Gittins type index for randomly evolving graphs (joint with E. Presman), pp. 567-588 in: From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift. Kabanov, Y.; Lipster, R.t; Stoyanov, J. (Eds.), Springer Verlag, 2006.
B35 The Optimal Stopping of Markov Chain and Recursive Solution of Poisson and Bellman Equations, pp. 609-621. in: From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift. Kabanov, Y.; Lipster, R.t; Stoyanov, J. (Eds.), Springer Verlag, 2006.
B36 The Existence and Uniqueness of Nash Equilibrium Point in an m-player Game "Shoot later, shoot first !'', 185-205, International J. of Game Theory, v. 34, 2, August, Springer-Verlag, 2006.
B37 A Generalized Gittins Index for Markov Chain and its Recursive Calculation, Statistics and Probability Letters. v. 54, Issue 3, pp. 375-551, 2010.
On Optimal Stopping of Random Sequences Modulated by Markov Chain, (joint with Ernest Presman), Theory of Probability and its Applications,
V. 54, Issue 3, pp. 375-551, 2010.
Optimal stopping of Markov chains and three abstract optimization problems, Stochastics, 83(4-6), 405–414, 2011.
Continue, Quit, Restart Probability Model, (joint with S. Steinberg), Annals of Operations Research, p. 1-24, v. 194, 2012, 2016.
Optimal stopping of Seasonal Observations and Projection of a Markov Chain, in “Inspired by Finance”, Springer, eds. Y. Kabanov, M. Rutkovski, T. Zariphopoulou, p. 535 – 543, 2014.
Elimination and Insertion Operations for Finite Markov Chains, joint with Constantine Steinberg, Modern Trends in Controlled Stochastic Processes – Vol. II, Luniver Press, Frome, 2016, Ed. A. Piunovskiy, pp. p. 130 – 139.
Basnet, A.J., Sonin, I.M. Parallel computing for Markov chains with islands and ports. Ann Oper Res (2017). https://doi.org/10.1007/s10479-017-2727-5.
Some Nontrivial Properties of a Formula for Compound Interest, joint with Mark Whitmeyer, Finance Research Letters, vol. 33, March 2020
Cups (joint with S. Molchanov), accepted in Arnold Journal, 2020

Published papers are copyrighted by the publisher. Users may make a single copy of published papers for educational purposes.

III. CONFERENCE PROCEEDINGS

Some problems of optimal choice under incomplete information (with V.I. Arkin and E.L. Presman). Abstracts of 1-st Conference on Optimal Planning and Control of Economics, Moscow, 1972, Sect. 3, 156--157.
Stochastic problems of optimal choice (with V.I. Arkin and E.L. Presman). Abstracts of the National Conference on Applied Probability and Statistics, Kishinev, 1972, 17--18, (in Russian).
On some problems of control of changes in technology (with V.I. Arkin and E.L. Presman). Ibid., 19--20, (in Russian).
The models of economical dynamics with R&D (with V.I. Arkin and E.L. Presman). Proceedings of VI-th National Conference on Control, 1974, 9--11, (in Russian).
The points of equilibrium in the game problems of optimal stopping (with E.L. Presman). Proceedings of 3-rd Soviet-Japanese Symposium on Probability Theory and Mathematical Statistics, Tashkent, 1975, 118--119.
The two-armed bandit problems in continuous time (with E.L. Presman). Abstracts of 2-nd International Vilnius Conference on Probability Theory and Mathematical Statistics, Vilnius, 1977, 2, 120--121.
On a model of resource allocation. Abstracts of the USSR-Poland Symposium on Mathematical Methods in Planning and Control in Economics, Moscow, 1977, 245--246.
The asymptotic behavior of the value function in a problem of sequential control with incomplete data (with E.L. Presman). Ibid,189--190.
Markov policies in infinite horizon dynamic programming problems with bounded value functions (with E.A. Feinberg). Abstracts of IV Soviet-Japan Symposium on Probability Theory and Mathematical Statistics, Tbilisi, 1982, 1, 209--210.
Two and many-armed bandit problems with infinite horizon (with E.L. Presman). Ibid., 2, 171--172.
Sequential control with incomplete information in the frame of the theory of adaptive systems (with V.I. Arkin and E.L. Presman). Summary of the Proceedings of the Workshop on Adaptation and Optimization, 1982, Moscow, 23--24.
Persistently nearly-optimal strategies in countable state Markov decision chains with the total reward criterion (with E.A. Feinberg). Abstracts of International conference "Stochastic Optimization'', Kiev, 1984, 74--76.
The problems of optimal control with incomplete data (with E.L. Presman). Ibid., 194--196. ???
The optimal control of Markov chains: stationary strategies. Proceedings of 18-th Symposium on Probability Theory and Mathematical Statistics, Bakuriani, 1984, 44, (in Russian).
The theorem on separation of jets and some properties of random sequences. Proceedings of 190th Symposium on Probability Theory and Mathematical Statistics, Bakuriani, 1985, 45--46 (in Russian).
The theorem on separation of jets and properties of random sequences of martingale type. Abstracts of 4-th International Conference on Probability Theory and Mathematical Statistics, Vilnius, 1985, 3, 149--150.
The existence of barriers for random sequences. Proceedings of 20-th Symposium on Probability Theory and Mathematical Statistics, Bakuriani, 1986, 51, (in Russian).
The theorem on separation of jets and related problems. Proceedings of 1-st World Congress of Bernoulli Society, (Tashkent, 1986), Moscow, 1990, 3, Sect. 11, p. 153. ???
On the asymptotic behavior of finite nonhomogeneous Markov chains. Abstracts of 5-th International Vilnius Conference on Probability Theory and Mathematical Statistics, Vilnius, 1989, 2, 159--160.
Projects selection in the presence of common blocks (with P.K. Katyshev). Abstracts of World Congress of International Econometric Society, Barcelona, 1990. ???
The sufficiency of Markov strategies in Markov Decision Processes. Abstracts of EURO XII/TIMS XXXI Joint International Conference on Operations Research/Management Sci., Helsinki, 1992.
Markov functionals in Markov Decision Processes. SIAM Conference on Control and Its Applications, Minneapolis,1992.
Replacement Models and optimal cycling in Markov Decision Processes. Abstracts of 34th ORSA/TIMS Joint National Meeting, San Francisco, 1992.
Cycles in Markov Decision Processes and Replacement Models. Abstracts of Conference on Applied Probability, INRIA/ORSA/TIMS, Paris, 1993.
Markov strategies for maximizing the probability of visiting. Abstracts of 37th Joint National Meeting, Boston, 1994.
The asymptotic behavior of finite nonhomogeneous Markov chains in forward and backward time. Short Communications. International Congress of Mathematicians. Zurich, 1994.
The asymptotic behavior of finite nonhomogeneous Markov chains, Int. conf on Satochastic Models & Optimal Stopping, Nazan Univ., Japan, 1994.
Two Simple Theorems in Optimal Stopping Problems, Applied Probability Conference INFORMS, Atlanta, Georgia, June 95.
Equivalent Stationary and Locally Stationary Policies in Stochastic Dynamic Programming, (jointly with E. Feinberg), INFORMS Conference,Washington, DC May 1996.
The Elimination Algorithm and its Applications, (jointly with J. Thornton), Nineth INFORMS Applied Probability Conference, Boston, MA, June 1997.
The elimination algorithm and its application to the optimal stopping problem, 36th IEEE Conference on decision and control, San Diego, CA, December 1997 .
The elimination algorithm for the optimal stopping problem: properties and applications, 10th INFORMS Applied Probability Conference, Ulm, Germany, 1999.
Recursive Computation of the Fundamental/Group Inverse Matrix of a Markov Chain, 5th World Congress of the Bernouilli Society for Mathematical Statistics and Probability, Guanajuato, Mexico, 2000.
The Existence and Uniqueness of Nash Equilibrium point in an m-player Game "Shoot Later, Schoot First !", First World Congress of the Game Theory Society, Bilbao, Spain, 2000.
The Optimal Stopping of ''Seasonal'' Observations, Abstracts, 11th INFORMS Applied Probability Conference, New York, USA, 2001, p.18.
The Existence and Uniqueness of Nash Equilibrium Point in an m-player Game "Shoot later, shoot first", (joint with E. Presman), Proceedings of Workshop on Optimal Stopping and Stochastic Games, Bedlewo, Poland, 2002, p.30.
On developments generated by a problem of A. N. Kolmogorov in the theory of Markov chains, Proceedings of International Conference "Kolmogorov and Contemporary Mathematics", Moscow State Univ., 2003.
A simple proof of an (Gittins) Index Theorem for Graphs (joint with E. Presman),, Proceedings of International Conference "Kolmogorov and Contemporary Mathematics", Moscow State Univ., 2003.
Abstract, p. 183, A Gittins index theorem for randomly evolving graphs. (R) (joint with E. Presman); In Abstracts of 6-th World Congress of the Bernoulli Society for Mathematical Statistics and Probability and 67-th Annual Meeting of the Institute of Mathematical Statistics, p.183, Barselona, July 26-31, 2004.
The Optimal Stopping of Markov Chain and Recursive Solution of Bellman Equation. (I), 40 min, Sixth International Petrozavodsk Conference: Probabilistic Methods in Discrete Mathematics , Petrozavodsk, Russia, June 2004.
The classes of an m-player Game ``Shoot later, shoot first” with an explicit and unique Nash Equilibrium Point, (joint with E. Presman), The Second World Congress of the Game Theory Society, Marseille, France, July 5 – July 9, 2004, http://WWW.GTS2004.ORG.
A generalized Gittins Index for a Markov Chain and its Recursive Calculation, In: International Workshop Optimal Stopping and Stochastic Control, August 22-26, 2005, Petrozavodsk, Russia, Extended Abstracts, p. 62-64.
Gittins Type Index for Randomly Evolving Graphs, (joint with E. Presman), In: International Workshop Optimal Stopping and Stochastic Control, August 22-26, 2005, Petrozavodsk, Russia, Extended Abstracts, p. 60-61.
An Inventory Optimization Model with Markov Modulated Commodity Prices (joint with J. Hill), Intern. Conf. on Management Sci., Univ. of Texas at Dallas, May 20 - 22, 2006.
A Decomposition-Separation Theorem for Markov chains. Conf. Markov Processes and Related Topics, Univ. of Wisconsin-Madison, July 10-13, 2006.