Pacific Journal of Mathematics

Conditional expectations associated with stochastic processes.

R. A. Brooks

Article information

Pacific J. Math., Volume 41, Number 1 (1972), 33-42.

First available in Project Euclid: 13 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G05: Foundations of stochastic processes


Brooks, R. A. Conditional expectations associated with stochastic processes. Pacific J. Math. 41 (1972), no. 1, 33--42.

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  • [1] R. A. Brooks, Linear Stochastic Control: A Hubert Space Measure Theoretic Approach, Ph. D. Dissertation, University of California, Irvine, 1970.
  • [2] J. L. Doob, Stochastic Processes, Wiley, New York, 1953.
  • [3] J. R. Fisher and E. B. Stear, Optimalnonlinearfilteringfor independentin- crement processes, IEEE Trans, on Inform. Theory, IT-3 (October 1967), 558-578.
  • [4] T. L. Gunckel III and G. F. Franklin, A general solution for linearsampled-data control, J. of Basic Engr., 85 (1963),197-201.
  • [5] P. D. Joseph and J. T. Tou, On Linear Control Theory, AIEE Trans, on Appl. and Indus., Part II, 80 (September 1961), 193-196.
  • [6] R. E. Kalman, On the General Theory of Control Systems, Proc. First IFAC Con- gress, pp. 481-493.
  • [7] R. E. Kalman, Contributions to the theory of optimal control, Bol. Soc. Mat. Mex., 5 (1960) 102-119.
  • [8] R. E. Kalman, A new approach to linear filtering and prediction problems, J. of Basic Engr., 82 (March 1960), 35-45.
  • [9] R. E. Kalman, et. al., Controllability of Linear Dynamical Systems, Contributions to Differential Equations, vol. 1, Wiley, New York, 1962.
  • [10] H. J. Kushner, On the dynamical equations of conditional probabilityfunctions, with applications to optimum stochastic control theory, J. Math. Anal. & Appl., 8 (April 1964), 332-344.
  • [11] H. J. Kushner, On the differential equations satisfied by conditional probability densities of Markov processes, with applications, SIAM J. of Control, 2 (1964), 106-119.
  • [12] H. J. Kushner, Dynamical equations for optimal nonlinear filtering, J. of Diff. Eq., 3 (April 1967), 179-190.
  • [13] J. P. LaSalle, The Time Optimal Control Problem, Contributions to Differential Equations, 5 (1960), 1-24. Princeton University Press, Princeton.
  • [14] M. Loeve, Probability Theory, 3rd ed., van Nostrand, Princeton, 1963.
  • [15] R. E. Mortensen, Optimal control of continuous-time stochastic systems, Electronics, Research Lab. Tech. Report, ERL-66-1, Univ. of Calif., Berkeley, August 1966.
  • [16] L. S. Pontryagin, et. al., The Mathematical Theory of Optimal Processes, Inter-
  • [17] R. J. Stuart, Continuous-timeNonlinear Filtering,Ph. D. dissertation, UCLA, 1969.