Research of Bero Roos

My main research interests are in the area of distributional approximations in probability theory and its applications. Motivated by the need for explicit approximation results for aggregate claims distributions in mathematical risk theory, I developed new techniques or improved existing methods for estimating the accuracy of distributional approximations mainly for compound distributions. For approximations in probability theory, explicit smoothness or concentration bounds of probability distributions are often needed. We derived several new upper bounds or improvements of some existing inequalities. One of the goals was to give optimal constants, whenever possible. Further interests lie in the area of stochastic point processes, extreme values, order statistics and records, stochastic orders, insurance and financial mathematics, theory of complex functions, and general inequalities.

Preprints and Articles

(Send me an email for pre- or reprints. There may be essential changes between preprint and published paper.)

[32]	On the Poisson approximation of random diagonal sums of Bernoulli matrices. Preprint: 25 pages, 2024.
[31]	Smoothness and Lévy concentration function inequalities for distributions of random diagonal sums. Theory of Probability and Mathematical Statistics, 111, 137−151, 2024. Preprint.
[30]	On the accuracy in a combinatorial central limit theorem: the characteristic function method. Teoriya Veroyatnostei i ee Primeneniya, 67(1), 150−175, 2022. (Also in: Theory of Probability and its Applications, 67(1), 118−139, 2022). Preprint, 21 pages, 2020.
[29]	New inequalities for permanents and hafnians and some generalizations. Preprint; version 1: 28 pages, 2019; version 2: 34 pages, 2020.
[28]	New permanent approximation inequalities via identities. Lithuanian Mathematical Journal, 60(2), 248−275, 2020. Preprint.
[27]	Generalization of a Hadamard type inequality for permanents. Linear Algebra and its Applications, 571, 58−77, 2019. Preprint.
[26]	Refined total variation bounds in the multivariate and compound Poisson approximation. Latin American Journal of Probability and Mathematical Statistics (ALEA), 14, 337−360, 2017. Preprint.
[25]	On Bobkov's approximate de Finetti representation via approximation of permanents of complex rectangular matrices. Proceedings of the American Mathematical Society, 143(4), 1785−1796, 2015. Preprint.
[24]	Closeness of convolutions of probability measures. Bernoulli, 16(1), 23−50, 2010. Preprint.
[23]	Poisson type approximations for the Markov binomial distribution. (Jointly with Vydas Čekanavičius). Stochastic Processes and their Applications, 119(1), 190−207, 2009. Preprint.
[22]	Maximal probabilities of convolution powers of discrete uniform distributions. (Jointly with Lutz Mattner). Statistics and Probability Letters , 78(17), 2992−2996, 2008. Preprint.
[21]	A shorter proof of Kanter's Bessel function concentration bound. (Jointly with Lutz Mattner). Probability Theory and Related Fields, 139(1−2), 191−205, 2007. Preprint. The original publication is available at www.springerlink.com.
[20]	Binomial approximation to the Markov binomial distribution. (Jointly with Vydas Čekanavičius). Acta Applicandae Mathematicae, 96(1−3), 137−146, 2007. Preprint. The original publication is available at www.springerlink.com.
[19]	On variational bounds in the compound Poisson approximation of the individual risk model. Insurance: Mathematics and Economics, 40(3), 403−414, 2007. Preprint.
[18]	An expansion in the exponent for compound binomial approximations. (Jointly with Vydas Čekanavičius). Lietuvos Matematikos Rinkinys, 46(1), 67−110, 2006. (See also in: Lithuanian Mathematical Journal, 46(1), 54−91, 2006). Preprint.
[17]	Compound binomial approximations. (Jointly with Vydas Čekanavičius). Annals of the Institute of Statistical Mathematics, 58(1), 187−210, 2006. Preprint. The original publication is available at www.springerlink.com.
[16]	On Hipp's compound Poisson approximations via concentration functions. Bernoulli, 11(3), 533−557, 2005. Preprint.
[15]	Two-parametric compound binomial approximations. (Jointly with Vydas Čekanavičius). Lietuvos Matematikos Rinkinys, 44(4), 443−466, 2004. (See also in: Lithuanian Mathematical Journal, 44(4), 354−373, 2004). Preprint.
[14]	Poisson approximation via the convolution with Kornya-Presman signed measures. Teoriya Veroyatnostei i ee Primeneniya, 48(3), 628−632, 2003. (See also in: Theory of Probability and its Applications, 48(3), 555−560, 2003). Preprint.
[13]	On error bounds for the approximation of random sums. (Jointly with Dietmar Pfeifer). Preprint No. 2003-04, March 2003, Fachbereich Mathematik, Schwerpunkt Mathematische Statistik und Stochastische Prozesse, Universität Hamburg. Presented at the XXXIV ASTIN Colloquium 2003 of the International Actuarial Association, 24−27 August 2003, Berlin, Germany.
[12]	Kerstan's method for compound Poisson approximation. The Annals of Probability, 31(4), 1754−1771, 2003. Preprint. ('Best Paper Award', 2003 Annual Conference of the German Mathematical Society (DMV)).
[11]	Poisson approximation of multivariate Poisson mixtures. Journal of Applied Probability, 40(2), 376−390, 2003.
[10]	On the distance between the distributions of random sums. (Jointly with Dietmar Pfeifer). Journal of Applied Probability, 40(1), 87−106, 2003.
[9]	Improvements in the Poisson approximation of mixed Poisson distributions. Journal of Statistical Planning and Inference, 113(2), 467−483, 2003. Preprint.
[8]	Kerstan's method in the multivariate Poisson approximation: an expansion in the exponent. Teoriya Veroyatnostei i ee Primeneniya, 47(2), 397−402, 2002. (See also in: Theory of Probability and its Applications, 47(2), 358−363, 2002). Preprint.
[7]	Multinomial and Krawtchouk approximations to the generalized multinomial distribution. Teoriya Veroyatnostei i ee Primeneniya, 46(1), 117−133, 2001. (See also in: Theory of Probability and its Applications, 46(1), 103−117, 2001). Preprint.
[6]	Sharp constants in the Poisson approximation. Statistics and Probability Letters, 52(2), 155−168, 2001. Preprint.
[5]	Binomial approximation to the Poisson binomial distribution: The Krawtchouk expansion. Teoriya Veroyatnostei i ee Primeneniya, 45(2), 328−344, 2000. (See also in: Theory of Probability and its Applications, 45(2), 258−272, 2000). Preprint.
[4]	Asymptotics and sharp bounds in the Poisson approximation to the Poisson-binomial distribution. Bernoulli, 5(6), 1021−1034, 1999.
[3]	On the rate of multivariate Poisson convergence. Journal of Multivariate Analysis, 69(1), 120−134, 1999.
[2]	Metric multivariate Poisson approximation of the generalized multinomial distribution. Teoriya Veroyatnostei i ee Primeneniya, 43(2), 404−413, 1998. (See also in: Theory of Probability and its Applications, 43(2), 306−315, 1998). Preprint.
[1]	A semigroup approach to Poisson approximation with respect to the point metric. Statistics and Probability Letters, 24(4), 305−314, 1995.
[0]	Metrische Poisson-Approximation (Metric Poisson Approximation). Doctoral thesis.(In German). Department of Mathematics, University of Oldenburg, 186 p., 1996.
[00]	Contributions to the approximation of some important distributions in the risk theory. Habilitation thesis. Department of Mathematics, University of Hamburg, 2002. (Contains the articles 2, 3, 5, 7−12, see above).