MSU Statistics and Probability Faculty Publications |

HABIB SALEHI
All Publications | Selected Publications |

1. The prediction theory of multivariate stochastic processes with continuous time, Doctoral dissertation, Indiana University, 1965.

2. A factorization algorithm for q * q matrix-valued functions on the real line R. Trans. Amer. Math. Soc. 124, 468-479, 1966.

3. The Hilbert space of square-integrable matrix-valued functions with respect to a *-finite non-negative hermitian measure and stochastic integrals. RM-151, Statistics and Probability, Michigan State University, 1966. (Abstract) Notices of the Amer. Math. Soc. 91, 632, 1966.

4. A transformation theorem on spectral measures. Proc. Amer. Math. Soc. 18, 610-613, 1967.

5. On the growth of a q-variate stationary stochastic process.Z. Wahrscheinlichkeitstheorie verw. Geb. 8, 140-147, 1967.

6. On the alternating projections theorem and bivariate stationary stochastic processes. Trans. Amer. Math. Soc. 128, 121-134, 1967.

7. The Hellinger square-integrability of matrix-valued measures with respect to a non-negative, hermitian measure. Ark. Mat. 7, 299-303, 1967.

8. Application of the Hellinger integrals to q-variate stationary stochastic processes. Ark. Mat. 7, 305-311, 1967.

9. Review of Differential Space, Quantum System and Prediction by N. Wiener, A. Siegel, B. Rankin and W. T. Martin, The M.I.T. Press, Anal. Math. Stat. 36, 1929-1931, 1967.

10. On detection of signals in q-variate stationary stochastic processes. J. Math. Anal. Appl. 21, 264-276, 1968.

11. On the Hellinger integrals and interpolation of q-variate stationary stochastic processes. Ark. Mat. 8, 1-6, 1968.

12. On interpolation of q-variate stationary stochastic processes. Pacific J. Math. 28,

183-191, 1969.

13. Interpolation of q-variate homogeneous random fields. J. Math. Anal. Appl. 25, 653-662, 1969.

14. The square-integrability of operator-valued functions with respect to a trace class-valued measure. RM-223, Statistics and Probability, MSU, 1969. (with V. Mandrekar).

15. Positive matrix H1/2 and hermitian matrix H functions are constant. Proc Amer. Math. Soc. 26, 469-470, 1970. (with G. D. Taylor).

16. The square-integrability of operator-valued functions with respect to a non-negative operator-valued measure and the Kolmogorov isomorphism theorem. Indiana Univ. Math. J. 20, 545- 563, 1970. (with V. Mandrekar).

17. Subordination of infinite-dimensional stationary stochastic processes. Ann. Inst. Henri Poincare B, 1, 115-130, 1970. (with V. Mandrekar).

18. Operator-valued wide-sense Markov processes and solutions of infinite- dimensional linear differential system driven by white noise. Math. System Theory 4, 340-356, 1970. (with V. Mandrekar).

19. On singularity and Legesque type decomposition for operator-valued measures. J. Multivariate Analysis 1, 167-185, 1971. (with V. Mandrekar).

20. On determination of the optimal factor of a nonnegative matrix-valued function. Proc. Amer. Math. Soc. 29, 383-389, 1971.

21. On a factorization theory of D. Lowdenslager. Proc. Amer. Math. Soc. 31,185-188, 1972. (with V. Mandrekar).

22. Stone's theorem for a group of unitary operators over a Hilbert space. Proc. Amer. Math. Soc. 31, 480-484, 1972.

23. Interpolation of q-variate weakly stationary processes over a locally compact abelian group. J. Multivariate Anal. 2, 307-331, 1972. (with J. K. Scheidt).

24. On the equivalence of Gaussian measures related to Banach space-valued processes, Technical Summary Report No. 1245, Mathematics Research Center, 1972. (with J. Kuelbs).

25. The spectrum and the law of large numbers for infinite dimensional non-stationary stochastic processes. J. Math. Anal. Appl. 41, 575-582, 1973.

26. Measurability of generalized inverses of random linear operators. SIAM J. Appl. Math., 25, 681-692, 1973. (with M. Z. Nashed).

27. On the structure of L2,M. Proceedings of the Conference on Vector and Operator Valued Measures and Applications, Snowbird, Utah, Academic Press, 199-207, 1973. (with V. Mandrekar).

28. A note on minimality and interpolation of harmonizable sequences. Bol. Soc. Mat. Mexicana, 18, 70-71, 1973.

29. On the bilateral linear predictor for minimal stationary stochastic processes. SIAM J. Appl. Math., 26, 502-507, 1974.

30. Factorization of positive operator valued functions on a Banach space. Indiana Univ. Math. J., 24, 103-113, 1974. (with A. G. Miamee).

31. Necessary and sufficient conditions for factorability of non-negative operator-valued functions on a Banach space. Proc. Amer. Math. Soc., 46, 43-50, 1974. (with A. G. Miamee).

32. Random solutions of nonlinear differential equations, Boll, Un. Math. Ital., 12, 209-213, 1975. (with R. Kannan).

33. Measurabilite du point fixe d'ne transformation aleatoire separable. C. R. Acad. Sci Paris, Ser. A., t-281, 663-664, 1975. (with R. Kannan).

34. Positive operators on a Banach space and the Fejer-Riesz theorem. Proc. Amer. Math. Soc., 56, 189-192, 1976. (with A. G. Miamee).

35. Measurability of solutions of nonlinear equations, Non-linear Functional Analysis and Differential Equations, Marcel Dekker, Inc., N.Y., 222-244, 1976. (with R. Kannan).

36. The factorization problem for positive operator valued functions on a Banach space and regularity of Banach space valued stationary stochastic processes. Sankhya, Ser. A, 39, 211-222, 1977.

37. Random nonlinear equations and monotonic nonlinearities. J. Math. Anal. Appl., 57, 234-256, 1977. (with R. Kannan).

38. On square root of a positive B(x,x*)-valued function, J. Multivariate Anal. 7, 535-550, 1977. (with A. G. Miamee).

39. A note on the product of operator-valued measures, Bol. Soc. Mat. Mexicana 22, 23-24, 1977. (with A. G. Miamee).

40. Harmonizability, V-boundedness and stationary dilation of stochastic processes. Indiana Univ. Math. J. 27, 37-50, 1978. (with A.G. Miamee).

41. On minimality of infinite dimensional stationary stochastic processes, Lecture Notes in Math. 656 Springer-Verlag, 119-128, 1978. (with A. G. Miamee).

42. On the factorization of a nonnegative operator valued function. Lecture Notes in Math. 656 Springer-Verlag, 129-137, 1978. (with A. G. Miamee).

43. Review of Innovation processes by Yu. A. Rozanov, Scripta Series in Math., Halstead Press, American Scientists 66, 378, 1978.

44. A note on product of operator-valued measures. Bol. Soc. Mat. Mexicana. 23, 23-24, 1979.

45. On bilateral prediction error matrix of a multivariate stationary stochastic process. SIAM J. Analysis. 10, 247-252, 1979. (with A. G. Miamee).

46. Algorithms for linear interpolator and interpolation error for minimal stationary stochastic processes. Ann. Probab. 7, 840-846, 1979.

47. On the prediction of periodically correlated stochastic processes. J. Multivariate Anal. 5, 167-179, 1980. (with A. G. Miamee).

48. Spatially homogeneous random evolutations. J. Multivariate Anal. 10, 141-180, 1980. (with D. Dawson).

49. The Continuation of Wiener's work on q-variate linear prediction and its extension to infinite-dimensional spaces. Norbert Wiener: Collected Work, Volume III, 307-338, edited by P. Masani, The MIT Press, 1981.

50. On regularity of homogeneous random fields, Prediction theory and harmonic analysis, 309-328, edited by V. Mandrekar and H. Salehi, North-Holland, 1983. (with A. R. Soltani).

51. Prediction theory and harmonic analysis, The Pesi Masani Volume, edited by V. Mandrekar and H. Salehi, North-Holland, 1983.

52. On normal dilation and spectrum of some classes of 2nd order processes. Bol. Soc. Mat. Mexicana 28, no. 1, 31-48, 1983. (with M. Slocinski).

53. On an explicit representation of the linear predictor of a weakly stationary stochastic sequence. Bol. Soc. Mat. Mexicana 28, 81-93, 1983. (with A. G. Miamee).

54. On subordination and linear transformation of harmonizable and periodically correlated processes. Probability Theory on Vector Spaces, Lecture Notes in Math. 1080; Springer-Verlag, 195-213, 1984. (with M. Pourahmadi).

55. Schauder basic measures in Banach and Hilbert spaces. Bol. Soc. Mat. Mexicana 29, 71-84, 1984. (with J. L. Abreu).

56. Spectral dilation of operator valued measures and its application to infinite dimensional harmonizable processes, Studia Math. 85, 257-297, 1987. (with A. Makagon).

57. Stationary fields with positive angles. J. Multivariate Anal. 22, 106-125, 1987. (with A. Makagon).

58. Infinite dimensional stationary sequences with multiplicity one. Ann. Acad. Sci. Fenn. Ser. A. I. Math. 12, 135-150, 1987. (with A. Makagon).

59. A note concerning spectral multiplicity one. Publ. Inst. Math. 44, 121-126, 1988. (with J. Gill).

60. Notes on infinite dimensional stationary sequences, Lecture Notes in Math. 1391 Springer-Verlag, 200-238, 1989. (with A. Makagon).

61. A state-space approach to transfer-function modeling. Statistical Inferences In Stochastic Processes, Vol. 6, 233-247, 1991. (with P. Brockwell and R. Davis).

62. An example of a harmonizable process whose spectral domain is not complete. Scand. J. Statist. 18, 249-254, 1991. (with A.G. Miamee).

63. On a class of Gauss-Galerkin methods for Markov processes. Nonstationary Stochastic Processes and Their Applications, World Scientific, 126-146, 1992. (with A. Hajjafar and D. Yen).

64. On bounded and harmonizable solutions of infinite order ARMA systems. New Directions in Time Series Analysis Part I, Volume 45 of IMA publication, Springer-Verlag, 193-213, 1992. (with A. Makagon).

65. Transfer-function models with non-stationary input. New Directions in Time Series Analysis Part I, Volume 45 of IMA publication, Springer-Verlag, 65-74, 1992. (with P. Brockwell and R. Davis).

66. Maximum likelihood transfer function modeling. Computer Science and Statistics: Proceedings of the 22nd Symposium on the Interface, Springer-Verlag, 303-306, 1992. (with P.J. Brockwell and R.A. Davis).

67. Statistical models for estimating daily streamflow in Michigan. Technical Report 91-4194, Water Resources Division, U.S. Department of Interior -- Geological Survey, 48 pages, 1992. (with D.J. Holtschlag).

68. Periodically correlated processes and their spectrum. Nonstationary Stochastic Processes and Their Applications, World Scientific, 147-164, 1992. (with A. Makagon and A.G. Miamee).

69. Autoregressive expansion of the linear predicator for stationary stochastic processes. Nonstationary Stochastic Processes and Their Applications, World Scientific, 176-193, 1992. (with J. Farshidi).

70. Structure of periodically distributed stochastic sequences. Stochastic Processes, A Festschrift in Honour of Gopinath Kallianpur, Springer-Verlag, 245-251, 1993. (with A. Makagon).

71. Infinite dimensional stationary sequences with multiplicity one; part II. Ann. Acad. Sci. Fenn. Serv. A.I. Math. 18, 203-210, 1993. (with A. Makagon).

72. Is the spectral domain of a periodically correlated sequence complete? RM 529,

Statistics and Probability, Michigan State University, 1993. (with A. Makagon).

73. Continuous time periodically correlated processes: spectrum and prediction. Stochastic Processes and Their Applications 49, 277-295, 1994. (with A. Makagon and A.G. Miamee).

74. Asymptotic solutions of linear partial differential equations of first order having random coefficients. Random Oper. and Stoch. Eqs. 2, 61-78, 1994. (with F.C. Hoppensteadt and R.Z. Khasminskii).

75. On asymptotic behavior of solutions of the wave equations perturbed by a fast

Markov process. Ulam Quarterly 2, no. 4, 40-56, 1994. (with A.V. Skorokhod).

76. Randomly perturbed Voltera intergral equations and some applications. Stochastics

and Stochastic Reports 54, 89-125, 1995. (with F. Hoppensteadt and A. Skorokhod).

77. An averaging principle for dynamical systems in Hilbert space with Markov random

perturbations. Stochastic Processes and their Applications 61, 85-108, 1996. (with F.

Hoppensteadt and A. Skorokhod).

78. On the asymptotic behavior of Markov chain with small random perturbations of

transition probabilities. Multidimensional Statistical Analysis and Theory of

Random Matrices: Proceedings of the Sixth Lukacs Symposium, Bowling Green

State University, 59-66, 1996. (with A.V. Skorokhod).

79. Markov chain with small random perturbations with applications to Bacterial

Genetics. Random Oper. and Stoch. Equ. 4, 205-227, 1996. (with F. Hoppensteadt

and A. Skorokhod).

80. On asymptotic behaviour of oscillatory solutions of operator differential equations

perturbed by a fast Markov process. Probabilistic Engineering Mechanic, 11,

251-255, 1996. (with A.V. Skorokhod); Also appeared under the same title with

some modification in Proceedings of The Third International Conference on

Stochastic Structural Dynamics, 4.20-4.26, 1997. (with A. Skorokhod).

81. Iterations of transformations with random perturbations. Proceedings of The Third International Conference on Stochastic Structural Dynamics, 9.44-9.50, 1997.

(with F. Hoppensteadt and A. Skorokhod).

82. Discrete time semigroups transformations with random perturbations. J. Dynamics

and Differential Equations 9, 463-505, 1997. (with F. Hoppensteadt and A. Skorokhod).

83. On optimal filtering of multitarget tracking systems based on point process observations. Random Oper. and Stoch. Equ. 5, 1-34, 1997. (with N. Portenko and A. Skorokhod).

84. Approximation of distribution laws in population genetics governed by Fokker-Plank equations. The Arabian J. for Science and Engineering 22, 2C, 3-15, 1997. (with N. Abrouk and D. Yen)

85. An application of orthogonal and biorthogonal systems in filtering problems. Theor. Probab. and Math. Stat. 56, 169-178, 1997. (with Y. Daletskii and A. Skorokhod).

86. Optimal filtering in target tracking in presence of uniformly distributed errors and false targets. Random Oper. and Stoch. Equ. 6, 213-240, 1998. (with N. Portenko and A. Skorokhod).

87. Filtering in multitarget systems with discrete time observation. Random Oper. and Stoch. Equ., 205-214, 1999. (with N. Portenko and A. Skorokhod).

88. Exact maximal inequalities for exchangeable systems of random variables. Theory of Probability and its Applications, 40, 1-13, 2000. (with S.A. Chobanyan).

89. On maximal inequality for exchangeable systems of random variables. Skorokhod's Ideas in Probability Theory, Proceedings of the Institute of Mathematics of The National Academy of Sciences of Ukraine (Edit. V. Korolyuk et al) 32, 119-125, 2000. (with S.A. Chobanyan).

90. On large deviations for dynamical systems randomly perturbed by a fast Markov processes. Theory of Stochastic Processes, Institute of Mathematics, National Academy of Sciences of Ukraine 6, 125-135, 2000. (with N.Partenko and A.Skorokhod).

91. On the tail estimation of the norm of Rademacher sums. Georgian Mathematical Journal 8, 267-244, 2001. (with S.A. Chobanyan).

92. Random Perutrbution Methods with Applications in Science and Engineering. Springer-Verlag, 2002. (with A.V. Skorokhod and F.C. Hoppensteadt).

93. On spectral domain of periodically correlated processes. To appear in Theory of Probability and its Application, 2005. (with A. Makagon, A.G. Miamee and A.R. Soltani).

94. General Maximal Inequalities Related to Strong Law of Large Numbers. Submitted to Zametki, October 2004. (with S.A. Chobanyan, S. Levental ).

95. On the Constant in Menshov-Radamacher inequality, to be submitted, Journal of Inequalities and Applications, March 2005. (with S.A. Chobanyan and S. Levental ).

07/21/05