Professor of
Mathematics and Statistics
Department of Mathematics and Statistics
American Mathematical Society
Mathematics ArXiv
Bogazici University Mathematics

Contact
information
Email:
nane@auburn.edu Phone: 334 8446595 Fax: 3348446555
Colloquiua
of Department of Mathematics and Statistics
Research interests
Probability and its Connections to Harmonic Analysis, Partial Differential Equations, Spectral Theory and Geometry. Social Links NSF/CBMS
Conference: Gaussian Random Fields, Fractals, SPDEs, and Extremes Principal Lecturer: Yimin Xiao, MSU
Foundation Professor Department
of Statistics and Probability, Michigan State University August
1213, 2022, University
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 spacetime fractional SPDEs. Submitted, 2022 3. Jebessa B. Mijena, E. Nane and A. Negash. Level of noise and long time behavior of spacetime fractional SPDEs in bounded domains, Submitted, 2022. 4. E. Nane and Y. Ni, Estimation of MeanReverting 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 threeparameter spacetime 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 spacetime 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 timesingular sources and perturbed orders. Fract. Calc. Appl. Anal. 25 (2022), no. 3, 11661198. 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 30, Issue 4: 13741413. 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. Timechanged Stochastic Control Problem and its Maximum Principle Theory. Probability and Mathematical Statistics, Vol. 41, Fasc. 2 (2021), pp. 193215. 6. N.H. Tuan, E. Nane and D. T. Dang. Analysis of a quasireversibility method for nonlinear parabolic equations with uncertainty data. Illinois J. Math. 65(4) (2021), 793845. 7. N. Guerngar, E. Nane, R. Tinaztepe, S. Ulusoy and H.W. van Vyk. Simultaneous inversion for the fractional exponents in the spacetime fractional diffusion equation, Fract. Calc. Appl. Anal. Vol. 24, No 3 (2021), pp818847. 2020 8. E. Nane and N. Guerngar. Moment bounds of a class of stochastic heat equations driven by spacetime colored noise in bounded domains. Stochastic Process. Appl. Volume 130, Issue 10, October 2020, Pages 62466270. 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 33393357. 10. S. Asogwa, M. Foodun, J. Mijena and E. Nane. Critical parameters for reactiondiffusion equations involving spacetime 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 nonexistence of global solution to a class of conformable timefractional stochastic equation. Statistics & Probability Letters, Volume 163, August 2020, 108792. 12. X. Meng and E. Nane. Spacetime fractional stochastic partial differential equations with Levy noise. Fract. Calc. Appl. Anal. Vol. 23, No 1 (2020), pp. 224249. 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. Blowup results for spacetime fractional stochastic partial differential equations. Potential Anal., Potential Analysis volume 53, pages 357386(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. 407426). 16. M. Foodun W. Liu
and E. Nane. Some
nonexistence results for a class of stochastic partial differential
equations. Journal
of Differential Equations, Volume 266, Issue 5, 15 February 2019, Pages 25752596. 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, 509519. 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, 423478. 19. E. Nane and Y. Ni. Path stability of the solution of stochastic differential equation driven by timechanged Levy noises. ALEA Lat. Am. J. Probab. Math. Stat. 15 (2018), no. 1, 479507. 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) 302338. 21. M. Kirane, E. Nane and N. H. Tuan. On a backward problem for multidimensional GinzburgLandau 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 4654. 2017 23. M. Foodun, N. Guerngar and E. Nane. Some properties of nonlinear fractional stochastic heat equations on bounded domains. Chaos, Solitons & Fractals Volume 102, September 2017, Pages 8693. 24. E. Nane and Y. Ni. Stability of the solution of stochastic differential equation driven by timechanged Levy noise. Proc. Amer. Math. Soc. 145 (2017), no. 7, 30853104. 25. S. Asogwa and E. Nane. Intermittency fronts for spacetime fractional stochastic partial differential equations in (d+1) dimensions. Stochastic Process. Appl. 127 (2017), no. 4, 13541374. 26. Y. Ҫenesiz, A. Kurt and E. Nane. Stochastic solutions of Conformable fractional Cauchy problems. Statistics & Probability Letters., Volume 124, May 2017, 126131. 27. M. Foodun and E. Nane. Asymptotic properties of some spacetime fractional stochastic equations. Mathematische Zeitschrift (2017), pp. 127. doi:10.1007/s0020901618343. 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 126134. 2016 29.
M.
Foodun, J.B. Mijena and E. Nane. Nonlinear
noise excitation for some spacetime fractional stochastic equations in
bounded domains. Fract.
Calc. Appl. Anal. Vol. 19, No 6 (2016), pp. 15271553. 30.
E. Nane and Y. Ni. Stochastic
Solution of Fractional FokkerPlanck Equations with SpaceTimeDependent
Coefficients. Journal of Mathematical Analysis
and Applications 442 (2016) 103116 31. M. D`ovidio and
E. Nane. Fractional Cauchy problems on compact manifolds. Stochastic Analysis and Applications, Vol. 34 (2016), No. 2, 232257. 32.
J.B. Mijena and E. Nane. Intermittence
and time fractional stochastic partial differential equations. Potential Anal. Vol. 44 (2016) 295312. 2015 33. J.B.
Mijena and E. Nane. Spacetime fractional stochastic partial differential equations.
Stochastic Process. Appl.
125, (2015) 33013326. 2014 34. J. B. Mijena and E. Nane. Correlation structure of timechanged Pearson diffusions. Statistics & Probability Letters. Volume 90, (2014), 6877. 35. J. B. Mijena and E. Nane. Strong analytic solutions of fractional Cauchy problems. Proceedings of the American Mathematical Society, 142 (2014), 17171731. 36. R. Banuelos, J. B. Mijena and E. Nane. Twoterm trace estimates for relativistic stable processes. Journal of Mathematical Analysis and Applications. Volume 410 (2014) 837846. 37. M. D`ovidio and E. Nane. Time dependent random fields on spherical nonhomogeneous surfaces. Stochastic Process. Appl. 124 (2014) 20982131. 2013 38.
Hassan Allouba
and E. Nane. Interacting timefractional and $\Delta^ν$ PDEs systems via
Browniantime and InversestableLevytime Brownian sheets. Stochastics and Dynamics. Vol. 13, No.1 (2013) pp.
1250012. 39.
M.M. Meerschaert, E. Nane and P. Vellaisamy. Transient Anomalous Subdiffusion on bounded domains. Proc. Amer. Math. Soc.
Vol. 141 (2013), No. 2, pp. 699710. 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. 10831093. 2012 41. Z.Q. Chen, M.M. Meerschaert and E. Nane. Spacetime fractional diffusion on bounded domains. Journal of Mathematical Analysis and Applications. Volume 393, Issue 2, 15 September 2012, Pages 479488. 42.
E. Nane. Fractional Cauchy problems on bounded domains: survey of recent results,
pp: 185198 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. αtime
fractional Brownian motion: PDE Connections and Local Times. ESAIM:P&S,
Vol. 16 (2012), 124. 2011 44.
M.M. Meerschaert, E. Nane and P. Vellaisamy. Distributedorder fractional
diffusions on bounded domains. Journal of Mathematical
Analysis and Applications. 379 (2011) 216228. 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, 16001620. 46. Arun Kumar, E. Nane and P. Vellaisamy. Timechanged Poisson processes. Statistics & Probability Letters. 81 (2011) 18991910. 2010 47. E. Nane, Y. Xiao and A. Zeleke. A strong law of large numbers with applications to selfsimilar stable processes. Acta Scientiarum Mathematicarum (Szeged) 76:34(2010), 697711. 48. E. Nane. Stochastic solutions of a class of higher order Cauchy problems in R^d. Stochastics and Dynamics, Volume: 10, Issue: 3(2010), 341366. 2009 49. B. Baeumer, M.M. Meerschaert and E. Nane. Spacetime duality for fractional diffusion. Journal of Applied Probability, Volume 46, Number 4 (2009), 11001115. 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 17441751. 51. B. Baeumer, M.M. Meerschaert and E. Nane. Brownian subordinators and fractional Cauchy problems. Trans. Amer. Math. Soc. 361 (2009), 39153930. 52. M.M. Meerschaert, E. Nane and P. Vellaisamy. Fractional Cauchy problems on bounded domains. The Annals of Probability , Vol. 37, (2009) No. 3, 9791007 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 11941202 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), 432445. 2. E. Nane. Higher order PDE`s and iterated processes, Trans. Amer. Math. Soc. 360 (2008), 26812692. 3. E. Nane. Isoperimetrictype inequalities for iterated Brownian motion in R^{n}, Statistics & Probability Letters , 78 (2008), 9095. 4. E. Nane. Symmetric αstable subordinators and Cauchy problems, IJPAM (International Journal of Pure and Applied Mathematics) Volume 42 no.2 (2008), 217225. 2007 1. E. Nane. Lifetime asymptotics of iterated Brownian motion in R^{n}, ESAIM:P&S, March 2007, Vol. 11, pp. 147160. 2006 1. E. Nane. Iterated Brownian motion in parabolashaped domains, Potential Anal. 24 (2006), no. 2, 105123. 2. E. Nane. Iterated Brownian motion in bounded domains in R^{n} , Stochastic Process. Appl. 116 (2006), no. 6, 905916. 3. E. Nane. Laws of the iterated logarithm for αtime Brownian motion,
Electron. J. Probab. 11
(2006), no. 18, 434459.
54. Stochastic models for spacetime fractional dynamics. Colloquium Talk. University of Nevada, Las Vegas, Nevada, November 2018. 55. Fractional Cauchy problems on compact manifolds. Special Session on Selfsimilarity and Longrange Dependence in Stochastic Processes. AMS Central Sectional Meeting, Ann Arbor, MI, October 2021, 2018. 56. Blowup results for spacetime fractional dynamics. Probability Seminar, Michigan State University, October 2018. 57. Stochastic Models for SpaceTime Fractional Dynamics. Joint International Meeting of Chinese Mathematical Society and American Mathematical Society. Fudan University, Shanghai, China, June11June 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. SpaceTime Fractional Stochastic Partial Differential Equations. Workshop on Future Directions in Fractional Calculus Research and Applications. October 1721, 2016. 61. Intermittence and spacetime fractional stochastic partial differential equations. Invited Seminar Talk at Cankiri Karatekin University, Cankiri, Turkey (July 2, 2015). 62. Intermittence and spacetime fractional stochastic partial differential equations. 2nd AnkaraIstanbul Workshop on Stochastic Processes(0634SP2015), Koc University, Istanbul, Turkey (June 1819, 2015). 63. Intermittence and spacetime fractional stochastic partial differential equations. International Conference on Applied Analysis and Mathematical Modelling, ICNAAM 2015. Yildiz Technical University, Istanbul, Turkey (June 812, 2015). 64. Intermittence and spacetime fractional stochastic partial differential equations. Invited Seminar Talk at Meliksah University, Kayseri, Turkey (May 28, 2015). 65. Intermittence and spacetime fractional stochastic partial differential equations. Invited Seminar Talk at Aksaray University, Aksaray, Turkey (May 29, 2015). 66. Intermittence and spacetime 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 2729, 2015 68. Intermittence and time fractional stochastic partial differential equations.SAMSA conference (Nov 2428, 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 1923, 2013). 70. CTRW Limits: Fractal Properties and Governing Equations. 8^{th} World Congress in Probability and Statistics. Istanbul, Turkey (July 914, 2012). 71. Continuous Time Random Walk Limits: Governing Equations and Fractal Dimensions. Probability Colloquium, Department of Mathematics, Selcuk University, Konya, Turkey (July 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. TimeChanged Processes and Cauchy Problems. Colloquium, Department of Mtahematics, University of Alabama at Birmingham, Birmingham, Al (September 2011). 75. Fractional Cauchy Problems for timechanged Processes. Tufts University Probability Seminar, Boston, MA (February 2011). 76. Cauchy Problems Solved by Running Subordinate Processes. Informs 2010 Annual meeting. Austin, Texas (November 710, 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 612, 2008. 82. Subordinated processes and Cauchy problems, Probability Seminar, Department of mathematics, University of Illinois, UrbanaChampaign, 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 αstable subordinators and Cauchy problems. Fourth International Conference of Applied Mathematics and Computing, (Plovdiv, Bulgaria, August 12  18, 2007). Some references. 88. Symmetric αstable subordinators and Cauchy problems. Department of Statistics and Probability Seminar, Michigan State University, March 2007. (twohour lecture). Some references. 89. Iterated Brownian motion: lifetime asymptotics and isoperimetrictype inequalities, Department of Statistics and Probability Colloquium, Michigan State University, September 2006. Some references. 91. Joint Mathematics Meeting, January 47, 2017. Hyatt Regency Atlanta and Mariott Atlanta Maqius, Atlanta, GA. 93. 8^{th} World Congress in Probability and Statistics. Istanbul, Turkey (July 914, 2012). 96. Informs 2010 Annual meeting. Austin, Texas (November 710, 2010) 99. Gaussian Analysis & SPDEs (October 2008) 100.Malliavin Calculus & Appl. (August 2008) 101.Twenty Ninth Midwest Probability Colloquium at the Northwestern University, October 1920, 2007. 
Erkan Nane
Last Modified: 03/06/2021