Arts & Sciences Program

Faculty & Staff

Dr. Jaap Geluk Head of Department and Professor of Mathematics Email: jgeluk@pi.ac.ae Phone: +971 2 607 5342 Office: 4017 (Umm Shaif)

Academic Qualifications

• Ph.D., Mathematics, State University, Leiden, the Netherlands 1983
• M.S. (Doctoraal examen), Mathematics, State University, Leiden, the Netherlands 1971

Experience

2005 to now	Professor of Mathematics, Petroleum Institute, Abu Dhabi
1971 to 2005	Erasmus University Rotterdam, Rotterdam, the Netherlands
Visiting/research positions	During my stay in Rotterdam, I had visiting positions at several universities: King Fahd University of Petroleum and Minerals (Dhahran, Saudi Arabia) 1986-1988, University of California Los Angeles 1989, American University of Sharjah (U.A.E.) 1998, Sultan Qaboos University (Muscat, Oman) 2000. I had research visits to Hong Kong University in 2005 and the University of Iowa in 2006.

Research Interests

Probability – limit theorems, heavy tailed distributions, convolutions

Analysis – Asymptotics, Regular variation, Tauberian Theorems, Integral transforms

Recent Publications

1. Geluk, J.; Frenk, J.B.G., (2011). Renewal theory for random variables with a heavy tailed distribution and finite variance Statistics and Probability Letters, 81, 1, 77 – 82.
2. Geluk, J., Second order results in subexponentiality submitted.
3. Ranjbar, V.; Amini, Y. M.; Geluk, J.; Bozorgnia, A., (2009) Correction on Asymptotic behavior of weighted sums of weakly negative dependent random variables, Journal of Sciences Islamic Republic of Iran 20, no. 3, 283.
4. Geluk, J., (2009). Some closure properties for subexponential distributions, Statistics and Probability Letters, 79, 8, 1108—1111.
   
5. Geluk, J., Tang, Q., (2009). Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables, Journal of Theoretical Probability, 22, 871-882. 
6. Geluk, J., Ng, K.G. (2006). Tail behavior of negatively associated heavy tailed sums, Journal of Applied Probability, 43, 587-593.
7. Geluk, J, de Vries, C.G. (2006). Weighted sums of subexponential random variables and asymptotic  dependence between returns on reinsurance equities, Insurance: Mathematics and  Economics 38, 39-56.
8. Geluk, J, (2004). Asymptotics in the symmetrization inequality, Statistics and Probability Letters, 69, 63-68/
9. Geluk, J, de Haan, L., (2002). On bootstrap sample size in extreme value theory, Publications de l’ Institut Mathematique, 71(85), 21-25.
10. Geluk, J, Peng, L., de Vries, C.G., (2000). Convolutions of heavy tailed random variables and applications to portfolio diversification and MA(1) time series, Advances in Applied Probability, 32, 1011-1026.
11. Geluk, J, Peng, L., (2000). Second order regular variation and the domain of attraction of stable distributions, Analysis, 20, 359–371.
12. Geluk, J., de Haan, L., (2000). Stable probability distributions and their domains of attraction: a direct approach, Probability and Mathematical Statistics, XX.1, 169-188.
13. Geluk, J., Peng, L., (2000). An adaptive optimal estimate of the tail index for MA(1) time series, Statistics and Probability Letters, 46, 217–227.
14. Geluk, J., de Haan, L., Resnick, S., Starica, C. (1997).Second order regular variation, convolution and the central limit theorem, Stochastic Processes and their Applications, 69, 139–159.
15. Ranjbar, V.; Amini, Y. M.; Geluk, J.; Bozorgnia, A. Correction on Asymptotic behavior of weighted sums of weakly negative dependent random variables, Journal of Sciences Islamic Republic of Iran 20 (2009), no. 3, 283.