Erkan Nane

                                                                                         Jack Brown  Assistant Professor of Mathematics and Statistics

                                                                                         Department of Mathematics and Statistics

                                                                                         Auburn University

                                                                                                            

                                                                                                                                                             


VITA

Math Resources

 

American Mathematical Society

Math Review

Mathematics Web

 

Mathematics ArXiv

Probability Web

Probability Abstracts

Electronic J. Probab. & ECP

 

 

Michigan

State

Stat&Probab

 

Purdue Mathematics Department

 

Bogazici University Mathematics



Other Links

Hotmail, Yahoo,

Local Weather

Webster's Dictionary

Turkey

YAGMUR SENA NANE (my daughter)

Google

 

                                                                                                                                                             

Contact information                                                                                                                      

     E-mail:  nane@auburn.edu                                                                                                                    

     Phone:   334 844-6595

     Fax:       334-844-6555

 

Teaching (Spring Semester,  2009)

      STAT 3010:   Statistics for Engineers and Scientists (MWF 9:00-950am. 318 Parker Hall)

      MATH 5/6670: Probability and Stochastic Processes (MWF 8:00-8:50am 228 Parker Hall)

 

Sample Teaching Materials:

 

 

 

Applied Time Series Analysis- Stat 4630-Spring -2011: Syllabus, exam1, exam2, final exam, project.  All files zipped.

 

Probability Theory-Math 7800-7810-Fall 2010, Spring2011: All files zipped.

Math7800: Syllabus, exam1, exam2, final exam,  hw1, hw2, hw3, hw4, hw5, hw6, hw7, hw8, hw9. 

Math 7810: Syllabus,  hand written notes, exam1, final exam,  hw1, hw2, hw3, hw4.

 

Statistics for Engineers and Scientists- Stat 3010-Fall 2010:  Syllabus, sample lecture notes, quiz1,  exam 1, practice exam 1.  All files zipped.

 

Statistics and Probability I- Stat 3600-Spring-2010: Syllabus, hand-written notes, exam1, final exam, quiz1, quiz2, quiz3, quiz4.   All files zipped.

 

Probability and Stochastic Processes Math 5/6680-Spring-2009: Syllabus, quiz1, quiz2, quiz3, quiz4, quiz5, quiz6, quiz7,  final exam.  All files zipped.

 

 

 

    

                                        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.        Strong analytic solutions of fractional Cauchy problems: (Joint with Jebessa B. Mijena).  Submitted.

2.        Space-time fractional diffusion on bounded domains: (Joint with Zhen-Qing Chen and M.M. Meerschaert ). Submitted.

3.        Fractal dimensions for continuous time random walk limits: (Joint with  M.M. Meerschaert, and Y. Xiao). Submitted.

 

 

  

To Appear/In press:

1.        E. Nane and Hassan Allouba.  Interacting time-fractional and $\Delta^ν$ PDEs systems via Brownian-time and Inverse-stable-Lévy-time Brownian sheets. (To appear)  Stochastics and Dynamics.

2.        E. Nane,  D. Wu and Y. Xiao. α-time fractional Brownian motion: PDE Connections and Local Times. (To appear) Esaim:P&S.

3.        M.M. Meerschaert, E. Nane and P. Vellaisamy. Transient Anomalous Sub-diffusion on bounded domains. (To appear)  Proceedings of the American Mathematical Society.

 

 

Publications Starting From

 

2012

 

1.       E. Nane. Fractional Cauchy problems on bounded domains:  survey of recent results, pp: 185—198  In Fractional Dynamics and Control. D. Baleanu,  J.A.T. Machado,  A.C.J. Luo (Editors). Springer (2012).

 

 

2011

1.        M.M. Meerschaert, E. Nane and P. Vellaisamy. Distributed-order fractional diffusions on bounded domains. Journal of Mathematical Analysis and Applications. 379 (2011) 216-228.

2.        M.M. Meerschaert, E. Nane and P. Vellaisamy. The fractional Poisson process and the inverse stable subordinator.  Electron. J. Probab.  Vol. 16 (2011), no. 59, 1600-–1620.

3.        Arun Kumar, E. Nane and P. Vellaisamy. Time-changed Poisson processes.  Statistics & Probability Letters. 81 (2011) 1899-1910.

 

 

2010

 

1.        E. Nane, Y. Xiao and A. Zeleke. A strong law of large numbers with applications to self-similar stable processes. Acta Scientiarum Mathematicarum (Szeged) 76:3-4(2010), 697-711.

2.        E. Nane.  Stochastic solutions of a class of higher order Cauchy problems in R^d.  Stochastics and Dynamics, Volume: 10, Issue: 3(2010) ,  341-366.

   

2009

 

1.        B. Baeumer,  M.M. Meerschaert and  E. Nane.  Space-time duality for fractional diffusion.  Journal of Applied Probability, Volume 46, Number 4 (2009), 1100-1115.

2.        E. Nane.  Laws of the iterated logarithm for a class of iterated processes, Statistics & Probability Letters ,Volume 79, Issue 16, 15 August 2009, Pages 1744-1751.

3.        B. Baeumer, M.M. Meerschaert and  E. Nane.  Brownian subordinators and fractional Cauchy problems.   Trans. Amer. Math. Soc. 361 (2009), 3915-3930.

4.        M.M. Meerschaert, E. Nane and P. Vellaisamy. Fractional Cauchy problems on bounded domains.  The Annals of Probability , Vol. 37, (2009) No. 3, 979-1007

5.        M.M. Meerschaert, E. Nane and Y.  Xiao. Correlated continuous time random walks.  Statistics & Probability Letters Volume 79, Issue 9, 1 May 2009, Pages 1194-1202

 

2008

 

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

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

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

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

 

2007

 

1.  E. Nane.  Lifetime asymptotics of iterated Brownian motion in Rn,  Esaim:P&S, March 2007, Vol. 11, pp. 147-160.

 

2006

 

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

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

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

 

 

 

Talks

 

 

1.        Continuous Time Random Walk Limits: Governing Equations and Fractal Dimensions. Colloquium, Department of Mathematical Sciences, University of Alabama at Huntsville (Nov 2011).

2.        Time-Changed Processes and Cauchy Problems. Colloquium, Department of Mtahematics, University of Alabama at Birmingham, Birmingham, Al (September 2011).

3.        Fractional Cauchy Problems for  time-changed Processes. Tufts University Probability Seminar, Boston, MA (February 2011).

4.        Cauchy Problems Solved by Running Subordinate Processes. Informs 2010 Annual meeting. Austin, Texas (November 7-10, 2010)

5.        Cauchy Problems in Bounded Domains and Iterated Processes. EMS2010, 28th European Meeting of Statisticians. EMS 2010, Piraeus, Greece, University of Piraeus (August 2010).

6.        Fractional Cauchy problems on bounded domains: survey of recent results. Third Conference on Nonlinear Science and Complexity. Ankara, Turkey, Çankaya University (July 2010).

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

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

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

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

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

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

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

14.     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.

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

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

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

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

 

Related Conferences 

1.        8th World Congress in Probability and Statistics. Istanbul, Turkey (July 9-14, 2012).

2.        NSF/CBMS Regional Research Conference in the Mathematical Sciences. University of Alabama in Huntsville, AL, June 4--8, 2012.

3.        4th International Conference on Porous Media & Annual Meeting of the International Society for Porous Media. Purdue University, West Lafayette, IN,  May 14-16, 2012.

4.        Informs 2010 Annual meeting. Austin, Texas (November 7-10, 2010)

5.        EMS2010, 28th European Meeting of Statisticians. EMS 2010, Piraeus, Greece, University of Piraeus (August 2010).

6.        Third Conference on Nonlinear Science and Complexity. Ankara, Turkey, Çankaya University (July 2010).

7.        Gaussian Analysis & SPDEs (October 2008)

8.        Malliavin Calculus & Appl. (August 2008)

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

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

 

 

 


Erkan Nane
Last Modified: 11/18/2011