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MSU Statistics and Probability Faculty Publications |
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ATMAH MANDREKAR All Publications |
1964 Multiplicity and representation theory of
purely non-deterministic processes and its applications. Thesis,
1965 Multiplicity and representation of purely
non-deterministic stochastic processes.
Theoria veryotnostell i ee primenueula
1966 Semigroups of isometries and the
representation and multiplicity of weakly stationary stochastic processes. Arkiv fur Mathematik 6,
1966 Applications of multiplicity theory of N-ple
Markov processes. Tech. Report 86, U of
1967 Quasi-invariance of analytic measures on compact groups. Bull. Amer. Math. Soc. 73, 915-920. (Jt. M. Nadkarni).
1967 On the linear prediction of stationary
processes indexed by lattice points. Tech. Report 100, U of
1967 Stationary spectral measures and their
applications. Tech. Report 102. U of
1968 On multivariate wide-sense Markov
processes.
1968 On a characterization of Bohr group. MRC Tech. Report 908, 1968. (Jt. D. J. Patil).
1969 On the realization of stochastic processes II. Sankhya, Series A, 31, 477-480. (Jt. H. Mann).
1969 On quasi-invariant ergodic measures on the circle group. J. of Functional Analysis 3, 157-163. (Jt. M. G. Nadkarni).
1969 On the existance of optimal stochastic controls. J. of Math. and Mechanics, 1151-1166. (Jt. H. Becker).
1970 On the connection between multiplicity
theory and O'Hanner's time domain analysis of weakly stationary processes. Essays in Probability and Statistics, Ed.
R.C. Bose, U of
1970 Harmonic analysis on certain vector spaces. Trans. Amer. Math. Soc., 213-231. (Jt. J. Kuelbs).
1970 Singular quasi-invariant measurers on the
line. Studia Mathematica,
1970 The square-integrability of operator-valued
functions with respect to a non-negative operator-valued measure and the
Kolmogorov isomorphism theorem.
1970 Subordination of infinite-dimensional
stationary stochastic processes. Ann. Inst. Henri Poincare,
1970 Operator-valued wide-sense Markov processes and solution of infinite differential system driven by white noise. Math. Systems Theory 4, 340-356. (Jt. H. Salehi).
1971 Spectral theory of H-valued processes. J. Multivariate Analysis 1, 1-16. (Jt. G. Kallianpur).
1971 On singularity and Lebesque-decomposition theory for operator-valued measures. J. Multivariate Analysis 1, 167-185. (Jt. H. Salehi).
1971 Wide-sense Martingale approach to linear
optimal estimation. Proc. Second Symp on
Non-Linear Estimation,
1972 On the factorization theory of D. Lowdenslager. Proc. Amer. Math. Soc. 31, 185-188. (with H. Salehi).
1972 Harmonic analysis for F-spaces with a basis. Trans. Amer. Math. Soc. 169, 113-152. (Jt. J. Kuelbs).
1972 Wiener closure theorems for abstract Wiener space. Proc. Amer. Math. Soc. 32, 169-172. (Jt. J. Kuelbs).
1972 Equivalence-singularity dichotomies from zero-one laws. Proc. Amer. Math. Soc. 31, 251-254. (Jt. R. D. LePage).
1972 Stable probability measures on Banach spaces. Studia Mathematica 42, 133-143 (Jt. A. Kumar).
1972 A characterization of oscillatory processes and their prediction. Proc. Amer. Math. Soc. 32, 280-284.
1973 Inversion formulas for Banach spaces with a basis. Trans. Amer. Math. 180, 143-169. (Jt. G. Hamedani).
1973 Multiplicity and Martingale approach to
linear estimation. Proceedings of Fifth
Annual
1973 A direct proof of Yu. A. Rozanov factorization theorem from the method of D. Lowdenslager. J. Multivariate Analysis 3, 137-140.
1973 Recursive optimal estimation of multiple Markov processes. Proc. 4th symposium on Non-linear estimation, 179-183. (Jt. K. Lee).
1974 On the multiple Markov property of Levy-Hida
for Gaussian processes.
1974 Wide-sense Martingale approach to linear
optimal filtering and smoothing.
1974 On the space L2M. Proc. Symp. on Vector-Values Measures and its applications. Academic Press. (Jt. H. Salehi).
1974 Domains of attraction of stable laws on Hilbert space. Studia Math., 149-162. (Jt. J. Kuelbs).
1974 The Markov property for generalized Gaussian
random fields. J. Inst. Fourier,
1974 Contributions to prediction theory and the
Harmonic analysis on vector spaces. J.
Math. and Physical Sciences,
1975 On likelihood ratios of measures given by Markov chains. Proc. Amer. Math. Soc. 377-380.
1975 Sur la quasi-invariance des measures sous
les translations. C.R.A.S.,
1976 Germ-field Markov property for multiparameter processes. Seminare de Probabilities X, Lecture Notes #511, Springer-Verlag. 78-85.
1976 On Bochner and Levy theorems in Orlicz spaces, Proc. Symposium on Measures on groups and Vector Spaces, Symposia Math. 21 Academic Press. i77-196.
1976 Central Limit Problem on Lp(p 2): Levy-Khinchine representation, Lecture Notes #528, Springer-Verlag.
1976 Quasi-invariance of measures under translations. Math. Zeit. 154, 19-29. (Jt. S. D. Chatterji).
1977 Central Limit Problem on Lp(p 2)11: Compactness of Infinitely divisible laws (Jt. G. Hamedani). J. Multivariate Analysis 7, 363-373.
1977 Levy-Khinchine representation and Banach space type. RM-374-MSU.
1978 Levy-Khinchine representation and Banach spaces of type and cotype. (Jt. G. Hamedani). Studia Math. 66. 207-214.
1978 On subordination of decomposible fields. Lecture Notes, #695, Springer-Verlag, 207-210.
1978 Characterization of Banach space through validity of Bochner Theorem. Lecture notes, #644, Springer-Verlag, 314-326.
1978 Singularity and absolute continuity of
measures. Proc. of Conference on
Functional Analysis
1978 Equivalence and singularity of Gaussian measures and applications. (with S. D. Chatterji). Probabilistic Analysis and Related Topics, Academic Press. Vol. 1, 169-197.
1979 The spaces Lp, M (0 < p ) (Jt. G. G. Hamedani) BIMS F, 3-8.
1979 On sums of independent random variables with values in Lp (2 p < ) (with E. Gine & J. Zinn). Probability in Banach spaces II. OBERWOLFACH Lecture Notes #709 p. 111-124.
1980 Central Limit Problem for symmetric case; convergence to non-Gaussian laws. (Jt. J. Zinn). Studia Math LXVII, 279-296.
1980 p-stable measures and absolutely summing operators (Jt. W. Linde and A. Weron). Probability Theory on Vector Spaces II, Lecture Notes #828, 167-178.
1981 Domains of attraction of stable laws on Banach spaces: Survey: Probability in Banach spaces III, Lecture Notes #860, 285-290.
1981 On accompanying laws theorem in Banach spaces: (Jt. A. Araujo, E. Gine and J. Zinn). Ann Prob. 9, 202-210.
1981 On -stable characterization of Banach spaces (Jt. A. Weron) J. Mult. Analysis 11, 572-580.
1981 Markov properties for random fields: Probabilistic Analysis and Related Topics, Academic Press Vol. III (Ed A. T. Barucha-Ried) 161-193.
1982 Radonifying maps related to p-stable
measures on Banach spaces (Jt. I W. Linde and A. Weron). Probability and Math. Stat. 2.,
1983 Non-deterministic random fields and Wold and Halmos decompositions for commuting isometries Prediction Theory and Harmonic Analysis North-Holland, 165-190. (Jt. G. Kallianpur).
1983 Commuting semigroups of isometries and Karhunen representation of Stationary random fields. Theory and application of Random Fields (with G. Kallianpur). Lecture notes in Control and Information Sciences 49 Springer-Verlag 126-145.
1983 Some remarks on various definitions of Feynman Integral, Prob. on Banach Spaces IV, OBERWOLFACH 1982, Lecture Notes #990, Springer-Verlag 170-177.
1983 Central Limit Problem and invariance principles on Banach Spaces. Seminaire des Probabilities XVII Lectures Notes #986, 425-496.
1983 Markov properties for random fields: Probabilistic Analysis and Related Topics, Academic Press Vol. III (Ed A. T. Barucha-Reid) 161-193.
1984 Stochastic Integral with respect to Gaussian processes. Lecture Notes in Math, 1089, 1984. Proc. OBERWOLFACH CONFERENCE ON Measure Theory 288-293.
1986 Censored data analysis in life testing and cosmology: Point process techniques (abstract) Stoch. Process and applns.
1988 On the validity of Beurling theorems in Polydiscs, Proc. Amer. Math. Society, 103, 145-148.
1988 On Beurling type invariant subspaces of L2 (T2) and their equivalence, (Jt. P. Ghatage). J. Operator Theory 20 83-89.
1988 Dispersion Distance and Prediction. Submitted for publication. (Jt. A. P. Taraporevala).
1989 On complex operator-valued O-U processes, T-positivity and innovations of Okabe and Masani (Jt. A. Makagon). J. of Multivariate Analysis, 27.
1989 On a limit theorem and invariance principle for symmetric statistics, J. of Prob. and Math. Stat. 10 (1989) 271-276.
1990 On the spectral representation of stable processes: Harmonizability and regularity (Jt. A. Makagon). Probability Theory and Related Fields 85 (1990) 1-11.
1990 Joint weak convergence on the whole line in
the truncation model. (Jt. B. Thelen)
Proc. of R.C. Bose Symposium on Prob., Stat. and Design of Exp. (1990) Wiley
Eastern, New
1990 Factorization through Hilbert-space and the dilation of L(X, Y)-valued measures,
(Jt. P. Richard). Studia Math. (107) 1993, 101-113.
1991 On multiple markov SaS processes, Stable
Processes and Related Topics (Ed Cambanis et al) Birkhauser,
1991 Multiplicative ARMA models for Random Fields (Jt. I. Basawa and P. Brockwell) Interface.
1991 On the spectral representation of sequences in Banach spaces (Jt. A. Makagon) Techn. Report 238, Center for Stochastic Processes UNC.
1991 Spectral theory of periodically and quasi periodically stationary SaS sequences. (Jt. H. Hurd) Tech. Report No. 349, Center for Stochastic Processes, UNC. Submitted for publication.
1992 Limit theorems for symmetric statistics of exchangeable random variables (Jt. R.F. Patterson) Stat. Prob. letters. 17, (1993) 157-161.
1992 Markov property of measure-indexed Gaussian random fields: Stochastic processes: A festschrift in honor of G. Kallianpur (1993) (Jt. S. Zhang). 253-262.
1992 Skorokhod integral and differentiation for Gaussian processes. Statistics & Probability Festschrift in honor of R.R. Bahadur, (Jt. S. Zhang). 395-410.
1992 Stable generalized moving averages (Jt. D. Surgailis, J. Rosinski and S. Cambanis). Prob. Theory and related topics, 97, p. 543-558.
1992 On stability of stochastic evolution equations (Jt. R. Khasminskii) in E.B. Dynkin Festschrift (ed M. Freidlin) Birkhauser 1994, p. 185-198.
1993 Ito-Ramer, Skorohod and Ogawa integrals with respect to Gaussian processes and their interrelationship (Jt. L. Gawarecki). Chaos Expansions, Wiener-Ito Integrals
and their applications Ed
Perez-Abreu and Houdre. CRC Press,
1994 Sample moments and symmetric statistics (Jt. M. Meerschaert) Pitman-Longman (Japan-USA Seminar on Stablity) (Ed H. Kuo and Kunita).
1994 Lyapounov type theorem for (deterministic) and stochastic evolution equations, Stochastic Analysis and applications to Physics, 219-237, NATO-ASI Series (Ed L. Streit et al) Kluwer, 1994.
1994 Girsanov type theorem for anticipative shifts (Jt. L. Gawarecki), Probability on Banach Spaces 9 (Ed Hoffman-Jorgensen et al) Birkhauser, 1994, p. 301-316.
1994 Remarks on AC-continuity and the spectral representation of stationary SaS sequences, Ulam Quarterly 2, no. 4, 27-39, 1994 (Jt. A. Makagon).
1995 Mathematical Work of Norbert Wiener, Invited paper to Notices, Amer. Math. Soc., 42, 664-669, 1995.
1995 Ultimate boundedness and invariant measures of stochastic evolution equations (Jt. R. Liu), Stochastic and Stochastic Reports, 56, (1996) 75-101.
1995 Consistent order estimator in periodic autoregressive models (Jt. H. Zhang) submitted.
1995 Stochastic semilinear evolution equations, Lyapunov function, stability and ultimate boundedness (Jt. R. Liu), Journal Math. Anal. and Applications, 212, (1997) 537-553.
1996 On weak solutions of stochastic PDE’s (Jt. A. Bhatt), (revised).
1997 Existence of weak solutions of stochastic differential equations and martingale solutions of stochastic semilinear equations (Jt. L. Gawarecki and P. Richard), Random Operators and SE, 7 (1999).
1997 Almost everywhere convergence and SLLN under rearrangements (Jt. S. Chobanyan), Stoch. Proc. and Rel. Topics: In memory of C. Cambanis. (Ed. Kallianpur etal), Burkhauser, (1998) 25-34.
1997 On the mixing structure of stationary increment self-similar SaS processes (Jt. D. Surgailis, J. Rosinski and S. Cambanis), submitted.
1997 Overview of Norber Wiener Centenary Congress (Jt. P. Masani). Proc. of NWCC, Symposia in Applied Math, 52, xv-xliv (1997), Ameri. Math. Soc.
1997 Stochastic Semilinear Evolution Equations, Lyopunov function, stability, etc. J. Math. Analysis and appl. 212, 537-553, (1997) (Jt. Liu).
1997 Weak solutions to SDE’s in Hilbert space IFIP Proc. (Jt. L. Gawarecki and
P. Richard) (1998).
1998 Kolmogorov SLLN under rearrangements for “Orthogonal” Random Varibales in a B-space (Jt. S. Chobanyan), J. Theoretical Prob., 13 (2000).
1998 Weak solutions
to SDE’s with application to semi-linear SDE’s,
Stochastics 98 (Jt. L. Gawarecki and P. Richard) (1998) 173-178.
1998 On Stabilization of Large (ecological) Systems, Statistics in the 21st
Century (ed. C.R. Rao and G. Szkely), Birkhauser (2000).
1998 Bayes Formula for Gaussian noise processes and applications to filtering problem (Jt. P. Mandal), SIAM J. of Conrol and Optimization, 39 (2000) 852-871.
1999 An approach to martingale problem for diffusion stochastic equations in Hilbert space
(Jt. A.V. Skorokhod), Stochastic Processes, 4 (20) (1998) p. 54-59.
1999 Bayes formula for optimal filter with n-ple Markov errors (Jt. P. Mandal), Act Appl. Math., 63 (2000) 245-252.
1999 Stochastic differential equations in Hilbert space with discontinuous drift (Jt. L. Gawarecki), Stochastic Processes, physics and geometry: new interplays II CMS conference proc. 29, Amer. Math. Soc. 199-205.
1999 Stochastic differential equations with discontinuous drift in Hilbert space with applications to infinite particle systems (Jt. L. Gawarecki), J. Mathematical Sciences, 105 (2001) 2550-2554.
2000 Estimation of hidden frequencies for 2-D stationary processes, (Jt. H. Zhang), J. Time Series Analysis, 22 (2001) 613-629.
2000 On Zakai Equation for filtering with Gaussian noise, (Jt. L. Gawarecki), Stochastics in finite/infinite dimensions (Ed. T. Hida at al) Trends Math Birkhauser (2001) 145-151.
2000 Proper moving average representations and outer functions in two variables, Georgian Math. J. (2001) 275-281.
2001 Numerical Solutions of stochastic heat equations perturbed by white noise, (Jt. R. Liu) Theory of Stochastic Processes, 7 (2001). .
2002 Statistics for engineers: experiential learning approach (Jt. R.L. Tummala and K. Morris) paper for Amer. Soc. Eng. Ed. Meeting (2002).
2003 An algorithm for the estimation of minimal cut and path sets from field failure data (Jt. A. Dharmadhikari). Stat & Prob. Letters, 58 (2002)
2004 Prokhorov blocks and strong law of large numbers under rearrangements (Jt. Chobanyan and Levental), J. Theor. Prob. (2004) 647-672.
2004 Non-linear filtering with Gaussian martingale noise: Kalman filter with fBM noise Festschrift for Herman Rubin (Jt. L. Gawarecki), IMS Lecture Notes Monograph, 45 (2004).
2004 Remark on “Instrumentation” problem of A.V. Balkrishnan (Jt. L. Gawarecki) J. Indian Stat. Assoc., 41 (2004).
2004 Existence and uniqueness of pathwise solutions for stochastic integral equations driven by Levy noise on separable Banach spaces (Jt. B. Ruediger), preprint 637, Univeristy of Bonn, Stochastics and Stochastic repeats, 2006.
2004 Le’vy noises and Stochastic integral on Banach spaces (jt. B. Ruediger) Stochastic
PDE’s and applications – VII (Ed. G. DaPralō and L. Tubaro (2005)
2005 Generalized OU processes on separable Banach spaces (jt. B. Ruediger) Proceedings of Ascona conference (Ed. F. Russeu et al) (2006)
2005 On computing approximation of correlation using Bernstein copula with probabilistic tools (jt. F. Abegaz, U. Naik-Nimbalkar) (submitted)
2006 Existence of mild solutions for SDE’s and
semilinear equations with non-Gaussian Le’vy processes (submitted) (jt.
2006 Linear SDE’s in the dual of multi-Hilbertiēn space (jt. Gawarecki L. and Rajeev B.) (submitted)
2006 Some applications of transference lemma to
compact vector summation (jt. A. Chobanyan,
2006 Modelling available bandwith for efficient QOS characterization of network (jt. A. Chobanyan, M. Mutka and Xi) (Submitted)
Papers Reprinted: The papers 2, 3 and 5 from the publication list are reprinted in Benchmark Papers in Computer Science and Electrical Engineering: Random Processes: Multiplicity Theory and canonical decompositions. Ed. A. Ephremides and J. B. Thomas, 1973.
The papers 1978(e) and 1983(e) have appeared as chapters in a book by invitation.
The paper 1983(e) consists of
lecture notes at
Lecture Notes (published)
Central Limit Problem and invariance principle on Banach spaces: Seminaire des Prob. XVII, 1983.
Lecture Notes (unpublished)
1. Multiparameter Gaussian Processes and their Markov Property, Department of Mathematics, EPF-Lausanne, 1975.
2. Second Order Processes: Multiplicity, prediction filtering and
factorization,
3. Stochastics Models in Biology.
4. Probability and Measure Theory Notes for 870-882-883 (1985). Revised (1988).
5. Existence
of weak solutions for SDE in Hilbert space Lehrstűle Math. V,
Research Reports on Censored Data
1. On asymptotic theory in censored
survival analysis without independent censoring RM-431 (1983)
2. On the asymptotic theory of estimation of the survival function in competing risks analysis. (with J. C. Gardiner) RM-432.
Books:
Prediction Theory and Harmonic Analysis (with H. Salehi) Editor.
Proceedings of NWCC, 1994, Symposia in Applied Mathematics, AMS (with P.R. Masani). Editor.