Erkan Nane

                                                                                         Associate Professor of Mathematics and Statistics

                                                                                         Department of Mathematics and Statistics

                                                                                         Auburn University

                                                                                                            

                                                                                                                                                             


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Contact information                                                                                                                      

     E-mail:  nane@auburn.edu                                                                                                                    

     Phone:   334 844-6595

     Fax:       334-844-6555

 

AMS Spring Southeastern Sectional Meeting Special Session on

Stochastic Processes and Related Topics

March 27-29, 2015, University of Alabama in Huntsville, Huntsville, Alabama

 

 

 

Teaching (Fall Semester,  2014)

      MATH 7820-90 Applied Stochastic Processes (MWF 09:00-09:50am. 318 Parker Hall)

     STAT 3600-80  Statistics and Probability I (MWF 08:00-08:50am236 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.        J.B. Mijena and E. Nane. Space-time fractional stochastic partial differential equations. Submitted

2.        J.B. Mijena and E. Nane.  Intermittence and  time fractional stochastic partial differential equations. Submitted

3.        M.  D’ovidio and E. Nane. Coordinate changed random fields on manifolds. Submitted.

 

 

 

  

To Appear/In press:

 

 

 

Publications Starting From

 

2014

 

1.        J. B. Mijena and E. Nane. Correlation structure of time-changed Pearson diffusions.  Statistics & Probability Letters, Volume 90, July 2014, Pages 68-77.

2.        J. B. Mijena and E. Nane. Strong analytic solutions of fractional Cauchy problems.   Proceedings of the American Mathematical Society, 142 (2014), 1717-1731.

3.        R. Bañuelos, J. B. Mijena and E. Nane. Two-term trace estimates for relativistic stable processes.  Journal of Mathematical Analysis and Applications. Volume 410 (2014) 837–846.

4.        M.  D’ovidio and E. Nane. Time dependent random fields on spherical non-homogeneous surfaces.  Stochastic Process. Appl. 124 (2014) 2098–2131.

 

 

 

2013

 

1.        Hassan Allouba and E. Nane. Interacting time-fractional and $\Delta^ν$ PDEs systems via Brownian-time and Inverse-stable-Lévy-time Brownian sheets. Stochastics and Dynamics.  Vol. 13,  No.1 (2013) pp. 1250012.

2.        M.M. Meerschaert, E. Nane and P. Vellaisamy. Transient Anomalous Sub-diffusion on bounded domains. Proc. Amer. Math. Soc. Vol. 141 (2013), No. 2, pp. 699–710.

3.        M.M. Meerschaert, E. Nane and Y.  Xiao. Fractal dimensions for continuous time random walk limits. Statistics & Probability Letters, Vol. 83 (2013), No. 4, pp. 1083–1093.

 

 

 

 

2012

 

1.         Z.-Q. Chen, M.M. Meerschaert and E. Nane.  Space-time fractional diffusion on bounded domains.  Journal of Mathematical Analysis and Applications. Volume 393, Issue 2, 15 September 2012, Pages 479–488.

2.       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).

3.        E. Nane,  D. Wu and Y. Xiao. α-time fractional Brownian motion: PDE Connections and Local Times.  ESAIM:P&S, Vol. 16  (2012), 1-24.

 

 

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 motionElectron. J. Probab. 11 (2006), no. 18, 434—459.

 

 

 

Talks

 

 

1.        Intermittence and  time fractional stochastic partial differential equations. SAMSA conference (Nov 24-28, 2014), Victoria Falls, Zimbabwe.

2.        CTRW Limits: Governing Equations and Fractal dimensions. NSF/CBMS Conference on ``Analysis of Stochastic Partial Differential Equations''  Michigan State University (August 19--23, 2013).

3.        CTRW Limits: Fractal Properties and Governing Equations.  8th World Congress in Probability and Statistics. Istanbul, Turkey (July 9-14, 2012).

4.        Continuous Time Random Walk Limits: Governing Equations and Fractal Dimensions. Probability Colloquium, Department of Mathematics, Selcuk University, Konya, Turkey (July 2012)

5.        Continuous Time Random Walk Limits in Bounded Domains.  4th International Conference on Porous Media & Annual Meeting of the International Society for Porous Media. Purdue University, West Lafayette, IN, May 14-16, 2012.

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

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

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

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

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

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

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

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

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

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

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

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

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

19.     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.

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

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

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

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

 

Related Conferences 

1.        Stochastic Processes and Related Topics.  AMS Spring Southeastern Sectional Meeting at the University of  Alabama in Huntsville from March 27-29, 2015 (Friday-Sunday).

2.        8th World Congress in Probability and Statistics. Istanbul, Turkey (July 9-14, 2012).

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

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

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

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

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

8.        Gaussian Analysis & SPDEs (October 2008)

9.        Malliavin Calculus & Appl. (August 2008)

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

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

 

 

 


Erkan Nane
Last Modified: 11/18/2011