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# People

Marjorie Hahn
Professor Emerita

Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
Bromfield-Pearson
Medford, MA 02155

Email @tufts.edu:
marjorie.hahn
Phone: 617-627-2363
Publications in Probability Grouped by Topic (partial listing):
Stochastic Analysis: Stochastic Differential Equations, Fokker-Planck-Kolmogorov Equations, Time-changed stochastic Processes
• SDEs driven by a time-changed Lévy process and their associated time-fractional order pseudo- differential equations. J. Theoret. Probab. 25 (2012), 262-279, with Kei Kobayashi and Sabir Umarov.
• Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion. Proc. Amer. Math. Soc.,139 (2011), 691-705, with Kei Kobayashi and Sabir Umarov.
• Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations. Invited survey paper for the first issue of the joint Versita-Springer volume of Fractional Calculus and Applied Analysis 14 (2011), 56-79, with Sabir Umarov.
• On time-changed Gaussian processes and their associated Fokker-Planck-Kolmogorov equations. Electronic Communications in Probability 16 (2011), 150-164, with Kei Kobayashi, Jelena Ryvkina, and Sabir Umarov.
Classes of Stochastic Processes
• Haar-based multi-resolution stochastic processes. To appear in J. of Theoret. Probab. (online first, Dec 2010) (DOI: 10.1007/s10959-010-0333-4), with Wei Zhang.
$$q$$-Gaussians
• On $$q$$-Gaussians and Exchangeability. J. of Physics A: Math. and Theoret. 43 (2010), with Xinxin Jiang and Sabir Umarov.
• On Generalized Leibniz Triangles and $$q$$-Gaussians, submitted (2012), with Xinxin Jiang and Sabir Umarov.
Empirical or Self-Normalized Central Limit Theorems
• Distinctions between the regular and empirical central limit theories for exchangeable random variables. Progress in Probability Series, Vol. 43 (1998), 111--144, Birkhauser, with Gang Zhang.
• Empirical central limit theorems for exchangeable random variables. Prob. Stat. Lett. 59 (2002), 75-81, with Xinxin Jiang.
• A self-normalized central limit theorem for ?-mixing stationary sequences. Statistics and Prob. Stat. Lett. 78 (2008), 1541-1547, with Xinxin Jiang.
• Testing serial non-independence by self-centering and self-normalizing. Statistics 43 (2009), 315-328, with Xinxin Jiang.
Approximation of Partial Sums
• Uniform local probability approximations: improvements on Berry-Esseen. Ann. Probab. 23, (1995), 446-463, with Michael J. Klass.
• Approximation of partial sums of arbitrary i.i.d. random variables and the precision of the usual exponential upper bound. Ann. Probab. 25, No.3, (1997), 1451-1470, with Michael J. Klass.
• Optimal upper and lower bounds for the upper tails of compound Poisson processes. J. Theoret. Probab. 11, No.2, (1998), 535-559, with Michael J. Klass.
• Central limit theorems for exchangeable random variables when limits are mixtures of normals. J. Theoret. Probab. 16 (2003), 543-571, with Xinxin Jiang.
Trimmed Sums With and Without Self-normalization
• Asymptotic normality of trimmed sums of phi-mixing random variables. Ann. Probab. 15, (1987), 1395-1418, with Jim Kuelbs and Jorge Samur.
• Universal asymptotic normality for conditionally trimmed sums. Stat. Prob. Lett. 2, (1988), 9-15, with Jim Kuelbs.
• A universal law of the iterated logarithm for trimmed and censored sums. Springer Lect. Notes in Math 1391, (1989), 82-98.
• The asymptotic distribution of self-normalized censored sums and sums-of-squares. Ann. Probab 18, (1990), 1284-1341, with Jim Kuelbs and Daniel C. Weiner.
• The asymptotic distribution of magnitude-winsorized sums via self-normalization. J. Theoret. Probab. 3, (1990), 137-168, with Jim Kuelbs and Daniel C. Weiner.
• Asymptotic behavior of partial sums: A more robust approach via trimming and self-normalization. In: Sums, Trimmed Sums, and Extremes, Progress in Probability 23, (1991), 1-54, Birkhauser, with Jim Kuelbs and Daniel C. Weiner.
• Asymptotic behavior of self-normalized trimmed sums: nonnormal limits. Ann. Probab. 20, (1992), 455-483, with Daniel C. Weiner.
• Asymptotic behavior of self-normalized trimmed sums: nonnormal limits II. J. Theoret. Probab. 5 (1992), 169-196 with Daniel C. Weiner.
Matching Theorems
• An Exposition of Talagrand's Mini-course on Matching Theorems. In: Proceedings of the Eighth International Conference on Probability in Banach Spaces, Progress in Probability Series 30, (1992), 3-38, Birkhauser, with Yongzhao Shao.
Operator-Stable Laws
• The multidimensional central limit theorem for arrays normed by affine transformations. Ann. Probab. 9, (1981), 611-623, with Michael J. Klass.
• Affine normability of partial sums of i.i.d. random vectors: a characterization. Z. Wahrscheinlichkeitstheorie 69, (1985), 479-505, with Michael J. Klass.
• Operator stable laws: series representations and domains of normal attraction. J. Theoretical Probability 2, (1988), 3-36, with William N. Hudson and Jerry A. Veeh.
Stables and Max-Stables
• On stability of probability laws with univariate stable marginals. Z. Wahrscheinlichkeitstheorie 64, (1983), 157-165, with Evarist Giné.
• Max infinitely divisible and max stable sample continuous processes. Probab. Theor. and Relat. Fields 87, (1990), 139-165, with Evarist Giné and Pirooz Vatan.
Random Sets
• Limit theorems for random sets: an application of probability in Banach space results. Lec. Notes in Math. 990, (1983), 112-135, with Evarist Giné and Joel Zinn.
• Characterization and domains of attraction of p-stable random compact convex sets. Ann. Probab. 13, (1985), 447-468, with Evarist Giné.
• The Lévy-Khinchin representation for random compact convex subsets which are infinitely divisible under Minkowski addition. Z. Wahrscheinlichkeitstheorie 70, (1985), 271-287, with Evarist Giné.
• M-infinitely divisible random compact convex sets. Lec. Notes in Math. 1153, (1985), 226-248, with Evarist Giné.
Central Limit Theorems in $$C$$ or $$D$$
• Conditions for sample-continuity and the central limit theorem, Ann. Probab. 5, (1977), 351-360.
• Sample-continuity of square-integrable processes. Ann. Probab. 5, (1977), 361-370, with Michael J. Klass.
• A note on the central limit theorem for square-integrable processes. Proc. Amer. Math. Soc. 69, (1977), 331-334.
• Central limit theorems in $$D[0,1]$$. Z. Wahrscheinlichkeitstheorie 44, (1978), 89-101.
Reconstruction of Laws from Projections; Radon Transform
• A characterization of the families of finite-dimensional distributions associated with countably additive stochastic processes whose sample paths are in D. Z. Wahrscheinlichkeithstheorie (1978), with Lester E. Dubins.
• The pointwise translation problem for the Radon transform in Banach spaces. Lect. Notes in Math. 828, (1980), 176-186, with Peter Hahn.
• Distances between measures from 1-dimensional projections as implied by continuity of the inverse Radon transform. Z. Wahrscheinlichkeitstheorie 70, (1985), 361-380, with Eric Todd Quinto.
Probability Volumes Edited
• Probability in Banach Spaces V. Lecture Notes in Math, vol. 1153 (1985), Springer-Verlag, with Anatole Beck, Richard Dudley, Jim Kuelbs, and Michael Marcus.
• Sums, Trimmed Sums and Extremes. Progress in Probability Series, vol. 23 (1991), Birkhauser, with David M. Mason and Daniel C. Weiner.
• Probability in Banach Spaces, 8. Progress in Probability Series, vol. 30 (1992), Birkhauser, with Richard Dudley and Jim Kuelbs.
• High-dimensional Probability. Progress in Probability Series, Vol. 43 (1998), Birkhauser, with Ernst Eberlein and Michel Talagrand.
Publications In Statistics Grouped by Topic
Spacings
• Maximum spacing estimates: A generalization and improvement of maximum likelihood estimates I. Progress in Probab. Vol. 35, Birkhauser, (1994), 417-431, with Yongzhao Shao.
• Limit theorems for the logarithm of sample spacings. Statist. Probab. Lett. 24 (1995), 121-132, with Yongzhao Shao.
• On a distribution-free test of fit for continuous distribution functions . Scand. J. Statist. 23,(1996), 63-73, with Yongzhao Shao.
• Strong consistency of maximum product of spacings estimates with applications in nonparametrics and in estimation of unimodal densities. Ann. Inst. Statist. Math. 51(1) (1999), with Yongzhao Shao.
• Maximum product of spacings method: a unified formulation with illustration of strong consistency. Illinois J. Math. 43(3) (1999), with Yongzhao Shao.
Maximum Likelihood Estimators
• Existence and strong consistency of maximum likelihood estimates for 1-dimensional exponential families. Statist. Probab. Lett. 28, (1996), 9-21, with Weiwen Miao.
• Existence of maximum likelihood estimates for multi-dimensional exponential families. Scand. J. Statist. 24, (1997), 1-16, with Weiwen Miao.
Estimation for Thick Tails
• On joint estimation of an exponent of regular variation and an asymmetry parameter for tail distributions. In: Sums, Trimmed Sums, and Extremes, Progress in Probability 30 (1991), 82-111, Birkhauser, with Daniel C. Weiner
Statistics Volumes Edited
• Probability in Banach Spaces V. Lecture Notes in Math, vol. 1153 (1985), Springer-Verlag, with Anatole Beck, Richard Dudley, Jim Kuelbs, and Michael Marcus.
• Sums, Trimmed Sums and Extremes Progress in Probability Series, vol. 23 (1991), Birkhauser, with David M. Mason and Daniel C. Weiner.
• Probability in Banach Spaces, 8. Progress in Probability Series, vol. 30 (1992), Birkhauser, with Richard Dudley and Jim Kuelbs.
• High-dimensional Probability. Progress in Probability Series, Vol. 43 (1998), Birkhauser, with Ernst Eberlein and Michel Talagrand.