People
Marjorie Hahn
Professor Emerita
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
BromfieldPearson
Medford, MA 02155
Email @tufts.edu:
marjorie.hahn
Phone: 6176272363
Publications in Probability Grouped by Topic (partial listing):
Stochastic Analysis: Stochastic Differential Equations, FokkerPlanckKolmogorov Equations, Timechanged stochastic Processes
 SDEs driven by a timechanged Lévy process and their associated timefractional order pseudo
differential equations.
J. Theoret. Probab. 25 (2012), 262279,
with Kei Kobayashi and Sabir Umarov.
 FokkerPlanckKolmogorov equations associated with timechanged fractional Brownian motion.
Proc. Amer. Math. Soc.,139 (2011), 691705,
with Kei Kobayashi and Sabir Umarov.
 Fractional FokkerPlanckKolmogorov type equations and their associated stochastic differential
equations. Invited survey paper for
the first issue of the joint VersitaSpringer volume of Fractional Calculus and Applied Analysis 14 (2011), 5679, with Sabir Umarov.
 On timechanged Gaussian processes and their associated FokkerPlanckKolmogorov equations.
Electronic Communications in Probability 16 (2011), 150164, with Kei Kobayashi, Jelena Ryvkina, and
Sabir Umarov.
Classes of Stochastic Processes
 Haarbased multiresolution stochastic processes. To appear in J. of Theoret. Probab. (online first, Dec 2010)
(DOI: 10.1007/s1095901003334), 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 SelfNormalized Central Limit Theorems
 Distinctions between the regular and empirical central limit theories for exchangeable random variables.
Progress in Probability Series, Vol. 43 (1998), 111144, Birkhauser, with Gang Zhang.
 Empirical central limit theorems for exchangeable random variables. Prob. Stat.
Lett. 59 (2002), 7581, with Xinxin Jiang.
 A selfnormalized central limit theorem for ?mixing stationary sequences. Statistics and
Prob. Stat. Lett. 78 (2008), 15411547, with Xinxin Jiang.
 Testing serial nonindependence by selfcentering and selfnormalizing.
Statistics 43 (2009), 315328, with Xinxin Jiang.
Approximation of Partial Sums
 Uniform local probability approximations: improvements on BerryEsseen.
Ann. Probab. 23, (1995), 446463, 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), 14511470, with Michael J. Klass.
 Optimal upper and lower bounds for the upper tails of compound Poisson processes.
J. Theoret. Probab. 11, No.2, (1998), 535559, with Michael J. Klass.
 Central limit theorems for exchangeable random variables when limits are mixtures of normals.
J. Theoret. Probab. 16 (2003), 543571, with Xinxin Jiang.
Trimmed Sums With and Without Selfnormalization
 Asymptotic normality of trimmed sums of phimixing random variables.
Ann. Probab. 15, (1987), 13951418, with Jim Kuelbs and Jorge Samur.
 Universal asymptotic normality for conditionally trimmed sums.
Stat. Prob. Lett. 2, (1988), 915, with Jim Kuelbs.
 A universal law of the iterated logarithm for trimmed and censored sums.
Springer Lect. Notes in Math 1391, (1989), 8298.
 The asymptotic distribution of selfnormalized censored sums and sumsofsquares.
Ann. Probab 18, (1990), 12841341, with Jim Kuelbs and Daniel C. Weiner.
 The asymptotic distribution of magnitudewinsorized sums via selfnormalization.
J. Theoret. Probab. 3, (1990), 137168, with Jim Kuelbs and Daniel C. Weiner.
 Asymptotic behavior of partial sums: A more robust approach via trimming and selfnormalization.
In: Sums, Trimmed Sums, and Extremes, Progress in Probability 23, (1991), 154, Birkhauser, with Jim Kuelbs and Daniel C. Weiner.
 Asymptotic behavior of selfnormalized trimmed sums: nonnormal limits.
Ann. Probab. 20, (1992), 455483, with Daniel C. Weiner.
 Asymptotic behavior of selfnormalized trimmed sums: nonnormal limits II.
J. Theoret. Probab. 5 (1992), 169196 with Daniel C. Weiner.
Matching Theorems
 An Exposition of Talagrand's Minicourse on Matching Theorems.
In: Proceedings of the Eighth International Conference on Probability in Banach Spaces, Progress in Probability Series 30, (1992), 338, Birkhauser, with Yongzhao Shao.
OperatorStable Laws
 The multidimensional central limit theorem for arrays normed by affine transformations.
Ann. Probab. 9, (1981), 611623, with Michael J. Klass.
 Affine normability of partial sums of i.i.d. random vectors: a characterization.
Z. Wahrscheinlichkeitstheorie 69, (1985), 479505, with Michael J. Klass.
 Operator stable laws: series representations and domains of normal attraction.
J. Theoretical Probability 2, (1988), 336, with William N. Hudson and Jerry A. Veeh.
Stables and MaxStables
 On stability of probability laws with univariate stable marginals.
Z. Wahrscheinlichkeitstheorie 64, (1983), 157165, with Evarist Giné.
 Max infinitely divisible and max stable sample continuous processes.
Probab. Theor. and Relat. Fields 87, (1990), 139165, 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), 112135, with Evarist Giné and Joel Zinn.
 Characterization and domains of attraction of pstable random compact convex sets.
Ann. Probab. 13, (1985), 447468, with Evarist Giné.
 The LévyKhinchin representation for random compact convex subsets which are infinitely divisible under Minkowski addition.
Z. Wahrscheinlichkeitstheorie 70, (1985), 271287, with Evarist Giné.
 Minfinitely divisible random compact convex sets.
Lec. Notes in Math. 1153, (1985), 226248, with Evarist Giné.
Central Limit Theorems in \(C\) or \(D\)
 Conditions for samplecontinuity and the central limit theorem,
Ann. Probab. 5, (1977), 351360.
 Samplecontinuity of squareintegrable processes.
Ann. Probab. 5, (1977), 361370, with Michael J. Klass.
 A note on the central limit theorem for squareintegrable processes.
Proc. Amer. Math. Soc. 69, (1977), 331334.
 Central limit theorems in \(D[0,1]\).
Z. Wahrscheinlichkeitstheorie 44, (1978), 89101.
Reconstruction of Laws from Projections; Radon Transform
 A characterization of the families of finitedimensional 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), 176186, with Peter Hahn.
 Distances between measures from 1dimensional projections as implied by continuity of the inverse Radon transform.
Z. Wahrscheinlichkeitstheorie 70, (1985), 361380, with Eric Todd Quinto.
Probability Volumes Edited
 Probability in Banach Spaces V.
Lecture Notes in Math, vol. 1153 (1985), SpringerVerlag, 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.
 Highdimensional 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), 417431, with Yongzhao Shao.
 Limit theorems for the logarithm of sample spacings.
Statist. Probab. Lett. 24 (1995), 121132, with Yongzhao Shao.
 On a distributionfree test of fit for continuous distribution functions .
Scand. J. Statist. 23,(1996), 6373, 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 1dimensional exponential families.
Statist. Probab. Lett. 28, (1996), 921, with Weiwen Miao.
 Existence of maximum likelihood estimates for multidimensional exponential families.
Scand. J. Statist. 24, (1997), 116, 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), 82111, Birkhauser, with Daniel C. Weiner
Statistics Volumes Edited
 Probability in Banach Spaces V.
Lecture Notes in Math, vol. 1153 (1985), SpringerVerlag, 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.
 Highdimensional Probability.
Progress in Probability Series, Vol. 43 (1998), Birkhauser, with Ernst Eberlein and Michel Talagrand.
