A strong approximation theorem for stochastic recursive algorithms

Journal of Optimization Theory and Applications

Volumn 100, Issue 3, 1999, Pages 499-513

  Borkar, V S ^a   Mitter, S K ^b  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Approximation of stochastic differential equations; Asymptotic behavior; Constant stepsize algorithms; Stochastic algorithms

Indexed keywords

APPROXIMATION ALGORITHMS; DIFFERENTIAL EQUATIONS;

APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATION; APPROXIMATION THEOREM; ASYMPTOTIC BEHAVIOUR; CONSTANT STEPSIZE ALGORITHM; RECURSIVE ALGORITHMS; STEP-SIZE ALGORITHMS; STOCHASTIC ALGORITHMS; STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTICS; STRONG APPROXIMATION;

STOCHASTIC SYSTEMS;

EID: 0033247487     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022630321574     Document Type: Article

References (17)

1. N, SIAM Journal on Control and Optimization, Vol. 29, pp. 999-1018, 1991.
2. d, SIAM Journal on Control and Optimization, Vol. 31, pp. 111-131, 1993.
3. 3. BORKAR, V. S., Probability Theory: An Advanced Course, Springer Verlag, New York, New York, 1996.
4. 4. HIRSCH, M. W., Convergent Activation Dynamics in Continuous-Time Networks, Neural Networks, Vol. 2, pp. 331-349, 1989.
5. 5. LIPTSER, R. S., and SHIRYAYEV, A. N., Statistics of Random Processes, I: General Theory, Springer Verlag, New York, New York, 1977.
6. 6. BHATTACHARYA, R. N., Asymptotic Behavior of Several Dimensional Diffusions, Stochastic Nonlinear Systems, Edited by L. Arnold and R. Lefever, Springer Verlag, Berlin, Germany, pp. 86-99, 1981.
7. 7. BORKAR, V. S., and GHOSH, M. K., Ergodic Control of Multidimensional Diffusions, II: Adaptive Control, Applied Mathematics and Optimization, Vol. 21, pp. 191-220, 1990.
8. 8. KUSHNER, H. J., Approximation and Weak Convergence Methods for Random Processes, MIT Press, Cambridge, Massachusetts, 1984.
9. 9. MEYN, S. P., and TWEEDIE, R. L., Markov Chains and Stochastic Stability, Springer Verlag, New York, New York, 1994.
10. 10. ARONSON, D. G., Bounds for the Fundamental Solution of a Parabolic Equation, Bulletin of the American Mathematical Society, Vol. 73, pp. 890-896, 1967.
11. 11. BORKAR, V. S., A Remark on the Attainable Distributions of Controlled Diffusions, Stochastics, Vol. 18, pp. 17-23, 1986.
12. 12. GŸONGI, I., Mimicking the One-Dimensional Marginal Distribution of Processes Having an Itô Differential, Probability Theory and Related Fields, Vol. 71, pp. 501-516, 1986.
13. 13. LADYZENSKAJA, O. A., SOLONNIKOV, V. A., and URAL'CEVA, N. N., Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, Vol. 23, 1968.
14. 14. COVER, T. M., and THOMAS, J. A., Elements of Information Theory, John Wiley, New York, New York, 1991.
15. 15. DEUSCHEL, J. D., and STROOCK, D., Large Deviations, Academic Press, New York, New York, 1989.
16. 16. PFLUG, G., Searching for the Best: Stochastic Approximation, Simulated Annealing, and Related Procedures, Identification, Adaptation, Learning, Edited by S. Bittanti and G. Picci, Springer Verlag, Berlin, Germany, pp. 514-549, 1996.
17. 17. GELFAND, S. B., Personal Communication, 1996.