Erkan Nane

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

 

 

 

 

    

Colloquiua of Department of Mathematics and Statistics

 

Research interests

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

 

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NSF/CBMS Conference: Gaussian Random Fields, Fractals, SPDEs, and Extremes

Principal Lecturer: Yimin Xiao, MSU Foundation Professor

Department of Statistics and ProbabilityMichigan State University

August 12-13, 2022University of Alabama in Huntsville

 

Publications

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

 

1.        E. Nane, and N. H. Tuan Continuity with respect to fractional order for a family of time fractional stochastic heat equations. Submitted, 2022.

2.        C.-S. Deng, W. Liu and E. Nane. Pathwise Blowup of space-time fractional SPDEs. Submitted, 2022

3.        Jebessa B. Mijena, E. Nane and A. Negash. Level of noise and long time behavior of space-time fractional SPDEs in bounded domains, Submitted, 2022.

 

4.        E. Nane and Y. Ni, Estimation of Mean-Reverting Stochastic Differential Equations with Compensated Poisson Jumps using Neural Networks, Submitted, 2021.

 

 

5.        B. Guo, E. Nane, N. H. Tuan, R.Wang. Invariant Measures for Discrete Wave Equations Driven by Superlinear Noise. Submitted 2020.

 

6.        P. D. Nguyen; E. Nane; O. Nikan; T. H. Nguyen. Approximation of the initial value for a damped nonlinear hyperbolic equations with random Gaussian white noise on the measurements Submitted 2020.

 

7.        Guerngar, E. Nane and S. Ulusoy. Inverse problem for a three-parameter space-time fractional diffusion equation. Submitted, 2018.

 

 

  

To Appear/In press:

 

 

 

 

 

 

Publications Starting From

 

2022

 

1.        N.T. Bao, E. Nane, H. H. Tuan. On a terminal value problem for stochastic space-time fractional wave equations, Mathematical Methods in the Applied Sciences. 2022

 

2.        Dien, Nguyen Minh; Nane, Erkan; Minh, Nguyen Dang; Trong, Dang Duc; Global solutions of nonlinear fractional diffusion equations with time-singular sources and perturbed orders. Fract. Calc. Appl. Anal. 25 (2022), no. 3, 1166-1198.

3.        V. Q. Mai, E. Nane, D. O'Regan, N. H. Tuan. Terminal value problem for nonlinear parabolic equation with Gaussian white noise. Electronic Research Archive, 2022, Volume 30Issue 4: 1374-1413.

 

4.        C.-S. Deng, W. Liu and E. Nane. Finite Time Blowup of Solutions to SPDEs with Bernstein Functions of the Laplacian. Potential Analysis, 2022.

 

 

2021

 

5.        E. Nane and Y. Ni. Time-changed Stochastic Control Problem and its Maximum Principle Theory. Probability and Mathematical Statistics, Vol. 41, Fasc. 2 (2021), pp. 193-215.

6.        N.H. Tuan, E. Nane and D. T. Dang. Analysis of a quasi-reversibility method for nonlinear parabolic equations with uncertainty data. Illinois J. Math. 65(4) (2021), 793-845.

7.        N. Guerngar, E. Nane, R. Tinaztepe, S. Ulusoy and H.-W. van Vyk. Simultaneous inversion for the fractional exponents in the space-time fractional diffusion equation, Fract. Calc. Appl. Anal. Vol. 24, No 3 (2021), pp818-847.

 

2020

8.        E. Nane and N. Guerngar. Moment bounds of a class of stochastic heat equations driven by space-time colored noise in bounded domains. Stochastic Process. Appl. Volume 130, Issue 10, October 2020, Pages 6246-6270.

9.        P. N. Duc, E. Nane, D. O'Regan and T. N. Huy. Approximation of mild solutions of a semilinear fractional differential equation with random noise. Proceedings of the American Mathematical Society, Volume 148, Number 8, August 2020, Pages 3339-3357.

10.    S. Asogwa, M. Foodun, J. Mijena and E. Nane. Critical parameters for reaction-diffusion equations involving space-time fractional derivatives. Nonlinear Differential Equations and Applications, 27, Article number: 30 (2020).

11.    E. Nane, E. R. Nwaeze, M. E. Omaba. Asymptotic behavior of solution and non-existence of global solution to a class of conformable time-fractional stochastic equation. Statistics & Probability Letters, Volume 163, August 2020, 108792.

12.    X. Meng and E. Nane. Space-time fractional stochastic partial differential equations with Levy noise. Fract. Calc. Appl. Anal. Vol. 23, No 1 (2020), pp. 224-249.

13.    E. Nane, Y. Xiao and A. Zeleke. Strong laws of large numbers for arrays of random variables and stable random fields. Journal of Mathematical Analysis and Applications, Volume 484, Issue 1, 1 April 2020, 123737

14.    S.Asogwa, J. B. Mijena and E. Nane. Blow-up results for space-time fractional stochastic partial differential equations. Potential Anal., Potential Analysis volume 53, pages 357-386(2020).

 

2019

 

15.    M.M. Meerschaert, E. Nane and P. Vellaisamy (2019). Inverse subordinators and time fractional equations. In Anatoly Kochubei, Yuri Luchko (Eds.), Basic Theory (pp. 407-426).

16.   M. Foodun W. Liu and E. Nane. Some non-existence results for a class of stochastic partial differential equations. Journal of Differential Equations, Volume 266, Issue 5, 15 February 2019, Pages 2575-2596.

2018

17.    A. Kumar and E. Nane. On Infinite Divisibility of the Distribution of Some Inverse Subordinators. Modern Stochastics: Theory and Applications, 2018, Vol. 5, No. 4, 509-519.

18.    D. T. Dang, E. Nane, D. M. Nguyen and N. H. Tuan. Continuity of solutions of a class of fractional equations. Potential Anal. 49 (2018), no. 3, 423-478.

19.    E. Nane and Y. Ni. Path stability of the solution of stochastic differential equation driven by time-changed Levy noises.  ALEA Lat. Am. J. Probab. Math. Stat. 15 (2018), no. 1, 479-507. 

20.    N. H. Tuan and E. Nane. Approximate solutions of inverse problems for nonlinear space fractional diffusion equations with randomly perturbed data. SIAM/ASA Journal on Uncertainty Quantification, 6(1), (2018) 302-338.

21.    M. Kirane, E. Nane and N. H. Tuan. On a backward problem for multidimensional Ginzburg-Landau equation with random data. Inverse Problems, 34 (2018) 015008 (21pp).

22.    E. Nane, N. H. Tuan and N. H. Tuan. A random regularized approximate solution of the inverse problem for the Burgers' equation. Statistics & Probability Letters. Volume 132, January 2018, Pages 46-54.

 

 

2017

 

23.    M. Foodun, N. Guerngar and E. Nane. Some properties of non-linear fractional stochastic heat equations on bounded domains. Chaos, Solitons & Fractals Volume 102, September 2017, Pages 86-93.

24.    E. Nane and Y. Ni. Stability of the solution of stochastic differential equation driven by time-changed Levy noise. Proc. Amer. Math. Soc. 145 (2017), no. 7, 3085-3104. 

25.    S. Asogwa and E. Nane. Intermittency fronts for space-time fractional stochastic partial differential equations in (d+1) dimensions. Stochastic Process. Appl. 127 (2017), no. 4, 1354-1374.

26.    Y. Ҫenesiz, A. Kurt and E. Nane. Stochastic solutions of Conformable fractional Cauchy problems. Statistics & Probability Letters., Volume 124, May 2017, 126-131.

27.    M. Foodun and E. Nane. Asymptotic properties of some space-time fractional stochastic equations. Mathematische Zeitschrift (2017), pp. 1--27. doi:10.1007/s00209-016-1834-3.

28.    N. H. Tuan and E. Nane. Inverse source problem for time fractional diffusion with discrete random noise. Statistics & Probability Letters. Volume 120, January 2017, Pages 126-134.

 

 

2016

 

29.   M. Foodun, J.B. Mijena and E. Nane. Non-linear noise excitation for some space-time fractional stochastic equations in bounded domains. Fract. Calc. Appl. Anal. Vol. 19, No 6 (2016), pp. 1527-1553.

30.   E. Nane and Y. Ni. Stochastic Solution of Fractional Fokker-Planck Equations with Space-Time-Dependent Coefficients. Journal of Mathematical Analysis and Applications 442 (2016) 103-116

31.    M. D`ovidio and E. Nane. Fractional Cauchy problems on compact manifolds. Stochastic Analysis and Applications, Vol. 34 (2016), No. 2, 232-257.

32.   J.B. Mijena and E. Nane. Intermittence and time fractional stochastic partial differential equations. Potential Anal. Vol. 44 (2016) 295-312.

 

 

 

2015

33.   J.B. Mijena and E. Nane. Space-time fractional stochastic partial differential equations. Stochastic Process. Appl. 125, (2015) 3301-3326.

 

2014

 

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

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

36.    R. Banuelos, 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.

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

 

 

 

2013

 

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

39.    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.

40.    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

 

41.    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.

42.   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).

43.   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

44.    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.

45.     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.

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

 

 

2010

 

47.    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.

48.    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

 

49.    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.

50.    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.

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

52.    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

53.    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

 

 

54.    Stochastic models for space-time fractional dynamics. Colloquium Talk. University of Nevada, Las Vegas, Nevada, November 2018.

55.    Fractional Cauchy problems on compact manifolds. Special Session on Self-similarity and Long-range Dependence in Stochastic Processes. AMS Central Sectional Meeting, Ann Arbor, MI, October 20-21, 2018.

56.    Blow-up results for space-time fractional dynamics. Probability Seminar, Michigan State University, October 2018.

57.    Stochastic Models for Space-Time Fractional Dynamics. Joint International Meeting of Chinese Mathematical Society and American Mathematical Society. Fudan University, Shanghai, China, June11-June 14, 2018.

58.    Stochastic Models for Fractional Dynamics. Invited Seminar talk at Shanghai Normal University, Shanghai, China, June 14, 2018.

59.    Stochastic Models for Fractional Dynamics. MANNA workshop, Santa Fe, NM, December 13 - 15, 2017.

60.    Space-Time Fractional Stochastic Partial Differential Equations.  Workshop on Future Directions in Fractional Calculus Research and Applications. October 17-21, 2016.

61.    Intermittence and space-time fractional stochastic partial differential equations. Invited Seminar Talk at Cankiri Karatekin University, Cankiri, Turkey (July 2, 2015).

62.    Intermittence and space-time fractional stochastic partial differential equations. 2nd Ankara-Istanbul Workshop on Stochastic Processes(0634SP2015), Koc University, Istanbul, Turkey (June 18-19, 2015).

63.    Intermittence and space-time fractional stochastic partial differential equations. International Conference on Applied Analysis and Mathematical Modelling, ICNAAM 2015. Yildiz Technical University, Istanbul, Turkey (June 8-12, 2015).

64.    Intermittence and space-time fractional stochastic partial differential equations. Invited Seminar Talk at Meliksah University, Kayseri, Turkey (May 28, 2015).

65.    Intermittence and space-time fractional stochastic partial differential equations. Invited Seminar Talk at Aksaray University, Aksaray, Turkey (May 29, 2015).

66.    Intermittence and space-time fractional stochastic partial differential equations. Invited Seminar Talk at Konya Selcuk University, Konya, Turkey (May 27, 2015).

67.    Intermittence and time fractional stochastic partial differential equations. AMS Spring Southeastern Sectional Meeting at the University of Alabama in Huntsville, March 27-29, 2015

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

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

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

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

72.    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.

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

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

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

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

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

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

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

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

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

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

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

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

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

86.    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.

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

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

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

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

Related Conferences 

91.    Joint Mathematics Meeting, January 4-7, 2017. Hyatt Regency Atlanta and Mariott Atlanta Maqius, Atlanta, GA.

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

93.    8th World Congress in Probability and Statistics. Istanbul, Turkey (July 9-14, 2012).

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

95.    4th International Conference on Porous Media & Annual Meeting of the International Society for Porous Media. Purdue University, West Lafayette, IN, May 14-16, 2012.

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

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

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

99.    Gaussian Analysis & SPDEs (October 2008)

100.Malliavin Calculus & Appl. (August 2008)

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

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


Erkan Nane
Last Modified: 03/06/2021