Erkan Nane

Assistant Professor

Department of Mathematics and Statistics

Auburn University

VITA

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Contact information                                                                                                                      

     E-mail:  nane@auburn.edu 

     Phone:   334 844-6595

     Fax:       334-844-6555

Teaching (Fall Semester,  2009)

      STAT 3600-090:   Probability and Statistics I (MWF 9:00-950am. 324 Parker Hall)

    MATH 2660-096: Topics in linear Algebra (T Th 9:30-10:45am. 320 Parker Hall)

Colloquiua of Department of Mathematics and Statistics

Research interests

      Probability and its Connections to Harmonic Analysis, Partial Differential Equations, Spectral Theory and Geometry.

Publications

Preprints (papers below are available at http://arxiv.org, click on the titles below to see).

1. Local times of multidimensional α-time fractional Brownian motion: (Joint with Yimin Xiao and Dongsheng Wu), Submitted.

2. A Strong Law of Large Numbers with Applications to Self-Similar Stable Processes:(Joint with Yimin Xiao, Aklilu Zeleke) Submitted (October 2008)

3. Higher order Cauchy problems in bounded domains: Submitted (October 2008)

To Appear/In press:

1. Space-time duality for fractional diffusion ( Joint with Boris Baeumer and M.M. Meerschaert) Journal of Applied Probability (To appear)

Publications Starting From

2009

1. Laws of the iterated logarithm for a class of iterated processes, Statistics & Probability Letters ,Volume 79, Issue 16, 15 August 2009, Pages 1744-1751.
2. Brownian subordinators and fractional Cauchy problems:(Joint with Boris Baeumer and  M.M. Meerschaert),   Trans. Amer. Math. Soc. 361 (2009), 3915-3930.
3. Fractional Cauchy problems on bounded domains: (Joint with M.M. Meerschaert and P. Vellaisamy), The Annals of Probability , Vol. 37, (2009) No. 3, 979-1007
4. Correlated continuous time random walks: (Joint with M.M. Meerschaert and Yimin Xiao), Statistics & Probability Letters Volume 79, Issue 9, 1 May 2009, Pages 1194-1202

2008

1.  Large deviations for local time fractional Brownian motion and applications: (Joint with M.M. Meerschaert and Yimin Xiao), Journal of Mathematical Analysis and Applications , 346 (2008),  432-445.

2. Higher order PDE’s and iterated processes, Trans. Amer. Math. Soc. 360 (2008), 2681-2692.

3.  Isoperimetric-type inequalities for iterated Brownian motion in Rⁿ, Statistics & Probability Letters , 78 (2008), 90-95.

4.    Symmetric α-stable subordinators and Cauchy problems, IJPAM (International Journal of Pure and Applied Mathematics) Volume 42 no.2 (2008), 217-225.

2007

1.   Lifetime asymptotics of iterated Brownian motion in Rⁿ, Esaim:PS, March 2007, Vol. 11, pp. 147-160.

2006

1.    Iterated Brownian motion in parabola-shaped domains, Potential Anal. 24 (2006), no. 2, 105--123.

2.    Iterated Brownian motion in bounded domains in Rⁿ ,  Stochastic Process. Appl. 116 (2006), no. 6, 905--916.

3.    Laws of  the iterated logarithm for α-time Brownian motion,  Electron. J. Probab. 11 (2006), no. 18, 434—459.

Talks

1. Domain of Attraction for stochastic processes, Probability Seminar, Auburn University, October 2008.

2. Fractional Cauchy Problems, Gaussian Analysis & SPDEs (October 2008), University Of Alabama in Huntsville, AMS Souteastern sectional meeting.

3.  Subordinated processes and Cauchy problems, Malliavin Calculus & Appl. Regional CBMS/NSF conference, Kent State University, OHIO, August 6-12, 2008.

4. Subordinated processes and Cauchy problems, Probability Seminar, Department of mathematics, University of Illinois, Urbana-Champaign, April 2008.

5. Iterated Brownian motion and a related class of processes. Department of Mathematics Colloquium,  University of Oregon,  Eugene, Oregon,  February 2008.

6. Iterated Brownian motion and a related class of processes. Department of Mathematics and Statistics Colloquium,  Auburn University,  Alabama,  February 2008.

7. Iterated Brownian motion and a related class of processes. Department of Mathematics and Statistics Colloquium, American University, Washington, DC,  February 2008.

8. Iterated Brownian motion and a related class of processes. Statistics Colloquium, Department of Statistics and Operations Research, University of North Carolina, Chapel Hill,  January 2008.

9. Symmetric α-stable subordinators and Cauchy problems. Fourth International Conference of Applied Mathematics and Computing, (Plovdiv, Bulgaria, August 12 - 18, 2007). Some references.

10. Symmetric α-stable subordinators and Cauchy problems. Department of Statistics and Probability Seminar,  Michigan State University, March 2007. (two-hour lecture). Some references.

11. Iterated Brownian motion: lifetime asymptotics and isoperimetric-type inequalities, Department of Statistics and Probability Colloquium,  Michigan State University, September 2006. Some references.

12. Iterated Brownian motion in open sets in Rⁿ, Probability Seminar at the Purdue University, October 2004.

Related Conferences 

1. 1. EMS2010, 28th European Meeting of Statisticians. EMS 2010, Piraeus, Greece, University of Piraeus (August 2010).
2.     .Gaussian Analysis & SPDEs (October 2008)

3. Malliavin Calculus & Appl. (August 2008)

4. Twenty Ninth Midwest Probability Colloquium at the Northwestern University, October 19--20, 2007.

5. Fourth International Conference of Applied Mathematics and Computing, (Plovdiv, Bulgaria, August 12 - 18, 2007)

Created by: Erkan Nane
Last Modified: 01/07/2009