Professor Jim Kuelbs

Ph.D., 1965, University of Minnesota 

Professor Emeritus 

Department of Mathematics 

(608) 263-4283


Associate Editor

Journal of Theoretical Probability

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: nonlogarithmic 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.

Path properties of multiple generations of a branching process

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.

Weak Convergence results for multiple generations of branching processes

(with Anand Vidayshankar), Journal of Theoretical Probability, 24(2011), pp. 376-396.

Asymptotic inference for high dimensional data

(with Anand Vidayshankar), Annals of Statistics, 38 (2010), 836-869. 

Half-region depth for stochatic processes

(with Joel Zinn), submitted, October 2012.

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), no. 66, 169-196.

Concerns with functional depth

(with Joel Zinn), ALEA, Lat. Am. Probab. Math. Stat (2013), vol. 10, no. 2, 831-855.

Empirical quantile CLTs for some self-similar processes

(with Joel Zinn), J. Theor. Probab. published online 4 September 2013

Research Interests

Probability, Stochastic Processes, Limit Theorems in Infinite Dimensional Settings