Professor James Kuelbs (Jim)

Ph.D., 1965, University of Minnesota
Professor Emeritus
Department of Mathematics

Selected Publications

Metric Entropy and Small Ball Problem for Gaussian Measures
(with Wenbo Li), Journal of Functional Analysis, 115, (1993)
Liminf Results for Gaussian Samples and Chung’s F.L.I.L.
(with Wenbo Li and Michel Talagrand), Annals of Probability, 22, (1994)
Dominating Points and Large Deviations for Random Vectors
(with Uwe Einmahl), Prob. Theor. Related Fields, 105, (1996)
Refined Gibbs Conditioning Principle for Certain Infinite Dimensional Statistics
(with Amir Dembo), Studia Sci. Math Hungarica, 34,(1998)
A General Compact LIL in Banach Spaces
(with Uwe Einmahl), Proceedings on High Dimensional Probability II, Birkhauser, Progress in Probability (1999), pp 259-276
A Functional LIL for Symmetric Stable Processes
(with W. Li and X. Chen), Annals of Probability, 28, (2000)
Large Deviation Probabilities and Dominating Points for Open Convex Sets: non-logarithmic behavior
Annals of Probability, vol. 28 (2000), pp1259-1279
Cluster Sets for a General LIL in Banach Spaces
(with Uwe Einmahl), Annals of Probability, vol. 29 (2001), pp 1451-1475
Rates of convergence for the Nummelin Conditional Weak Law of large numbers
(with Ana Mela), Stoch. Proc. and their Applications, 98 (2002), pp. 229-252.
Moderate deviation probabilities for open convex sets: non-logarithmic behavior
(with Uwe Einmahl), Ann. Probab., 32 (2004), pp. 1316-1355.
A functional LIL for stochastic integrals and the Levy area process
(with Wenbo Li) Journal of Theoretical Probability, 18 (2005), pp. 261-290.
Another view of the CLT in Banach spaces
(with Joel Zinn), Journal of Theoretical Probability, 21 (2008), 982-1029.
Interpolation spaces and the CLT in Banach spaces
(with Joel Zinn), IMS Collections, High Dimensional Probability V: The Luminy Volume, 5 (2009), 73-83.
Functional limit laws of Strassen and Wichura type for multiple generations of a branching process
(with Anand Vidyashankar), IMS Collections, High Dimensional Probability V: The Luminy Volume, 5 (2009), 131-152.
Asymptotic inference for high dimensional data
(with Anand Vidayshankar), Annals of Statistics, 38 (2010), 836-869.
Weak Convergence results for multiple generations of branching processes
(with Anand Vidayshankar), Journal of Theoretical Probability, 24(2011), pp. 376-396.
A CLT for empirical processes involving time-dependent data
(with Thomas Kurtz and Joel Zinn), Ann. Probab. (2013), vol. 41, no. 2, 785-816.
Cluster sets for partial sums and partial sum proceses
(with Uwe Einmahl), Ann. Probab.(2014), vol. 42, no. 3, 1121-1160.
Empirical quantile CLT’s for time dependent data
(with Joel Zinn), Progress in Probab, HDP-VI (2013), vol. 66, 167-194.
Concerns with functional depth
(with Joel Zinn), ALEA, Lat. Am. Probab. Math. Stat (2013), vol. 10, no. 2, 831-855.
Half-region depth for stochastic processes
(with Joel Zinn), J. Multivar Anal. (2015), vol. 142, 86-105.
Empirical quantile CLTs for some self-similar processes
(with Joel Zinn), J. Theor. Probab. (2015), vol. 28, 313-336.
Limit Theorems for Quantile and Depth Regions for Stochastic Processes
(with Joel Zinn), High Dimensional probability VII, Progress in Probability (2016), vol. 71, 255-280.
Convergence of quantile and depth regions
(with Joel Zinn), Stochastic Processes and their Applications (2016), vol. 126, no. 12, 3681-3700.

Research Interests

Probability, Stochastic Processes, Limit Theorems in Infinite Dimensional Settings