Contact
information
Email:
nane@auburn.edu
Phone: 334 8446595
Fax:
3348446555
Research interests
Probability and its
Connections to Harmonic Analysis, Partial Differential Equations, Spectral
Theory and Geometry.
Social Links
Google
Scholar
Research Gate
Linkedln
PubMed
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.
Q.
Meng, Y. Wang, P. Kloeden, E. Nane, Y. Ni. The asymptotic behavior of
solutions for stochastic differential equations driven by timechanged Levy
noises. Submitted, 2023.
2.
E.
Nane, and N. H. Tuan. Continuity with respect to fractional order for a
family of time fractional stochastic heat equations. Submitted, 2022.
3.
C.S.
Deng, W. Liu and E. Nane. Pathwise
Blowup of spacetime fractional SPDEs. Submitted, 2022.
4.
E.
Nane and Y. Ni, Estimation of MeanReverting Stochastic Differential
Equations with Compensated Poisson Jumps using Neural Networks, Submitted,
2021.
To Appear/In press:
Publications Starting From
2023
1.
R.Wang,
E. Nane and N. H. Tuan. Evolution
Systems of Probability Measures for Nonautonomous KleinGordon Ito Equations
on Z^N. Bulletin des Sciences Mathematiques,
Volume 189, December
2023, 103348.
2.
Jebessa
B. Mijena, E. Nane and A. Negash. Level of noise and long time
behavior of spacetime fractional SPDEs in bounded domains, Discrete and
Continuous Dynamical Systems Series S, 2023, Volume 16, Issue 10: 25592588.
3.
Guerngar, E. Nane, S. Ulusoy and H.W. van Vyk. A uniqueness determination
of the fractional exponents in a threeparameter fractional diffusion,
Fractional Differential Calculus. Volume 13, Number 1 (2023), 87104.
4.
Tran
Bao, Ngoc; Nane,
Erkan; Huy
Tuan, Nguyen. On a terminal value problem for
stochastic spacetime fractional wave equations. Math. Methods Appl. Sci. 46 (2023), no. 1, 12061226.
5.
E. Eroglu, E. Nane. GNSSbased TEC data
modeling with the solar wind parameters. Indian J Phys (June
2023) 97(7):19731980.
6.
C.S. Deng, W. Liu and E. Nane. Finite Time Blowup in L^2
Sense of Solutions to SPDEs with Bernstein Functions of the Laplacian. Potential Analysis,
(2023) 59:565588.
7.
E. Eroglu, E. Nane and U. D. Goker. Seismoionospheric
anomalies related to the Mw 6.6, 20 July 2017 earthquake in Bodrum, Turkey. Natural
Hazards, Volume 117, Issue 2, Pages 15211539, June 2023.
2022
8.
Phuong,
Nguyen Duc; Nane,
Erkan; Nikan,
Omid; Nguyen
Anh Tuan. Approximation of
the initial value for damped nonlinear hyperbolic equations with random
Gaussian white noise on the measurements. AIMS
Math. 7 (2022), no.
7, 1262012634.
9.
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.
10.
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.
2021
11.
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.
12.
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.
13.
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
14.
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.
15.
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.
16.
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).
17.
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.
18.
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.
19.
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
20.
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
21. 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).
22. 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
23. 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.
24. 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.
25.
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.
26.
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.
27.
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).
28. 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
29.
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.
30.
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.
31.
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.
32.
Y.
Ҫenesiz, A. Kurt and E. Nane. Stochastic
solutions of Conformable fractional Cauchy problems. Statistics & Probability
Letters., Volume 124, May 2017, 126131.
33.
M. Foodun and E.
Nane. Asymptotic properties of some spacetime fractional stochastic
equations. Mathematische
Zeitschrift (2017), pp. 127. doi:10.1007/s0020901618343.
34.
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
35. 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.
36. E. Nane and Y. Ni. Stochastic
Solution of Fractional FokkerPlanck Equations with SpaceTimeDependent
Coefficients. Journal of Mathematical
Analysis and Applications 442 (2016) 103116
37. M. D`ovidio and
E. Nane. Fractional Cauchy problems on compact manifolds. Stochastic Analysis and Applications, Vol. 34 (2016), No. 2, 232257.
38.
J.B. Mijena and E. Nane. Intermittence
and time fractional stochastic partial differential equations. Potential Anal. Vol. 44 (2016) 295312.
2015
39. J.B. Mijena
and E. Nane. Spacetime fractional stochastic partial differential equations.
Stochastic Process. Appl.
125, (2015) 33013326.
2014
40.
J.
B. Mijena and E. Nane. Correlation structure of timechanged Pearson diffusions. Statistics & Probability
Letters. Volume 90, (2014), 6877.
41.
J.
B. Mijena and E. Nane. Strong analytic solutions of fractional Cauchy problems. Proceedings of the American Mathematical Society,
142 (2014), 17171731.
42.
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.
43.
M. D`ovidio and
E. Nane. Time dependent random fields on spherical nonhomogeneous surfaces.
Stochastic Process. Appl.
124 (2014) 20982131.
2013
44.
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.
45.
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.
46.
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
47.
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.
48. 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).
49. E. Nane, D. Wu and Y. Xiao. αtime
fractional Brownian motion: PDE Connections and Local Times. ESAIM:P&S,
Vol. 16 (2012), 124.
2011
50.
M.M. Meerschaert, E. Nane and P. Vellaisamy. Distributedorder fractional
diffusions on bounded domains. Journal of Mathematical
Analysis and Applications. 379 (2011) 216228.
51. 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.
52.
Arun
Kumar, E. Nane and P. Vellaisamy. Timechanged
Poisson processes. Statistics & Probability
Letters. 81 (2011) 18991910.
2010
53. 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.
54. 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
55. B. Baeumer, M.M. Meerschaert and E. Nane. Spacetime
duality for fractional diffusion. Journal of
Applied Probability, Volume 46, Number 4 (2009), 11001115.
56. 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.
57. B. Baeumer, M.M. Meerschaert and E. Nane. Brownian
subordinators and fractional Cauchy problems. Trans. Amer. Math. Soc. 361 (2009),
39153930.
58. M.M. Meerschaert, E. Nane and P. Vellaisamy. Fractional
Cauchy problems on bounded domains. The Annals of Probability ,
Vol. 37, (2009) No. 3, 9791007
59. 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
60. 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.
61. E. Nane. Higher order PDE`s and iterated processes, Trans. Amer. Math. Soc. 360
(2008), 26812692.
62. E. Nane. Isoperimetrictype
inequalities for iterated Brownian motion in R^{n}, Statistics & Probability
Letters , 78 (2008), 9095.
63. E. Nane. Symmetric
αstable subordinators and Cauchy problems, IJPAM (International Journal of Pure and Applied
Mathematics) Volume 42 no.2 (2008), 217225.
2007
64. E. Nane. Lifetime
asymptotics of iterated Brownian motion in R^{n}, ESAIM:P&S,
March 2007, Vol. 11, pp. 147160.
2006
65. 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
66. E. Nane. Iterated
Brownian motion in parabolashaped domains, Potential Anal. 24 (2006), no. 2, 105123.
67. E. Nane. Iterated
Brownian motion in bounded domains in R^{n } , Stochastic Process. Appl. 116 (2006), no. 6, 905916.
68. E. Nane. Laws of the iterated logarithm for αtime Brownian motion,
Electron. J. Probab. 11
(2006), no. 18, 434459.
1.
Stochastic
models for spacetime fractional dynamics. Colloquium Talk. University of
Nevada, Las Vegas, Nevada, November 2018.
2.
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.
3.
Blowup
results for spacetime fractional dynamics. Probability Seminar, Michigan
State University, October 2018.
4.
Stochastic
Models for SpaceTime Fractional Dynamics. Joint International Meeting of
Chinese Mathematical Society and American Mathematical Society. Fudan
University, Shanghai, China, June11June 14, 2018.
5.
Stochastic
Models for Fractional Dynamics. Invited Seminar talk at Shanghai Normal
University, Shanghai, China, June 14, 2018.
6.
Stochastic
Models for Fractional Dynamics. MANNA
workshop, Santa Fe, NM, December 13  15, 2017.
7.
SpaceTime Fractional
Stochastic Partial Differential Equations. Workshop on Future Directions in Fractional Calculus
Research and Applications. October 1721, 2016.
8.
Intermittence
and spacetime fractional stochastic partial differential equations. Invited
Seminar Talk at Cankiri Karatekin University, Cankiri, Turkey (July 2, 2015).
9.
Intermittence
and spacetime fractional stochastic partial differential equations. 2nd AnkaraIstanbul
Workshop on Stochastic Processes(0634SP2015), Koc University, Istanbul, Turkey (June
1819, 2015).
10.
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).
11.
Intermittence
and spacetime fractional stochastic partial differential equations. Invited
Seminar Talk at Meliksah
University, Kayseri, Turkey (May 28, 2015).
12.
Intermittence
and spacetime fractional stochastic partial differential equations. Invited
Seminar Talk at Aksaray University,
Aksaray, Turkey (May 29, 2015).
13.
Intermittence
and spacetime fractional stochastic partial differential equations. Invited
Seminar Talk at Konya Selcuk University,
Konya, Turkey (May 27, 2015).
14.
Intermittence
and time fractional stochastic partial differential equations. AMS Spring
Southeastern Sectional Meeting at the University of Alabama in Huntsville,
March 2729, 2015
15.
Intermittence
and time fractional stochastic partial differential equations.SAMSA conference (Nov 2428, 2014),
Victoria Falls, Zimbabwe.
16.
CTRW Limits:
Governing Equations and Fractal dimensions. NSF/CBMS Conference on
``Analysis of Stochastic Partial Differential Equations'' Michigan State
University (August 1923, 2013).
17.
CTRW
Limits: Fractal Properties and Governing Equations. 8^{th} World
Congress in Probability and Statistics. Istanbul, Turkey (July
914, 2012).
18.
Continuous
Time Random Walk Limits: Governing Equations and Fractal Dimensions.
Probability Colloquium, Department of Mathematics, Selcuk University, Konya, Turkey
(July 2012)
19.
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 1416, 2012.
20.
Continuous
Time Random Walk Limits: Governing Equations and Fractal Dimensions.
Colloquium, Department of Mathematical Sciences, University of Alabama at
Huntsville (Nov 2011).
21.
TimeChanged
Processes and Cauchy Problems. Colloquium,
Department of Mtahematics, University of Alabama at Birmingham, Birmingham,
Al (September 2011).
22.
Fractional
Cauchy Problems for timechanged Processes. Tufts University Probability
Seminar, Boston, MA (February 2011).
23.
Cauchy
Problems Solved by Running Subordinate Processes. Informs 2010
Annual meeting. Austin, Texas (November 710, 2010)
24.
Cauchy
Problems in Bounded Domains and Iterated Processes. EMS2010, 28th European
Meeting of Statisticians. EMS 2010, Piraeus,
Greece, University of Piraeus (August 2010).
25.
Fractional
Cauchy problems on bounded domains: survey of recent results. Third Conference on Nonlinear Science and Complexity.
Ankara, Turkey, Cankaya University (July 2010).
26.
Domain of Attraction for
stochastic processes, Probability Seminar, Auburn University, October 2008.
27.
Fractional
Cauchy Problems, Gaussian Analysis & SPDEs (October 2008),
University Of Alabama in Huntsville, AMS Souteastern sectional meeting.
28.
Subordinated
processes and Cauchy problems, Malliavin Calculus & Appl. Regional CBMS/NSF
conference, Kent State University, OHIO, August 612, 2008.
29.
Subordinated processes
and Cauchy problems, Probability Seminar, Department of mathematics,
University of Illinois, UrbanaChampaign, April 2008.
30.
Iterated
Brownian motion and a related class of processes. Department of Mathematics
Colloquium, University of Oregon, Eugene, Oregon, February
2008.
31.
Iterated
Brownian motion and a related class of processes. Department of Mathematics
and Statistics Colloquium, Auburn University, Alabama,
February 2008.
32.
Iterated
Brownian motion and a related class of processes. Department of Mathematics
and Statistics Colloquium, American University, Washington, DC,
February 2008.
33.
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.
34.
Symmetric
αstable subordinators and Cauchy problems. Fourth
International Conference of Applied Mathematics and Computing,
(Plovdiv, Bulgaria, August 12  18, 2007). Some references.
35.
Symmetric
αstable subordinators and Cauchy problems. Department of Statistics
and Probability Seminar, Michigan State University, March 2007.
(twohour lecture). Some references.
36.
Iterated Brownian
motion: lifetime asymptotics and isoperimetrictype inequalities,
Department of Statistics and Probability Colloquium, Michigan State
University, September 2006. Some references.
37.
Iterated Brownian motion
in open sets in R^{n}, Probability Seminar at the Purdue University,
October 2004.
Related Conferences
1.
Joint Mathematics Meeting,
January 47, 2017. Hyatt Regency Atlanta and Mariott Atlanta
Maqius, Atlanta, GA.
2.
Stochastic Processes and Related Topics. AMS
Spring Southeastern Sectional Meeting at the University of Alabama in
Huntsville from March 2729, 2015 (FridaySunday).
3.
8^{th} World Congress in Probability and
Statistics. Istanbul, Turkey (July 914, 2012).
4.
NSF/CBMS Regional Research Conference in the Mathematical
Sciences. University of Alabama in Huntsville, AL, June 48,
2012.
5.
4th International Conference on Porous Media & Annual
Meeting of the International Society for Porous Media. Purdue
University, West Lafayette, IN, May 1416, 2012.
6.
Informs 2010 Annual meeting. Austin, Texas (November 710, 2010)
7.
EMS2010, 28th European Meeting of Statisticians. EMS 2010, Piraeus, Greece, University of Piraeus (August
2010).
8.
Third Conference on Nonlinear Science and Complexity. Ankara, Turkey, Cankaya University (July 2010).
9.
Gaussian Analysis & SPDEs (October 2008)
10.
Malliavin Calculus & Appl. (August 2008)
11.
Twenty Ninth Midwest Probability Colloquium
at the Northwestern University, October 1920, 2007.
12.
Fourth International Conference of Applied Mathematics and
Computing, (Plovdiv, Bulgaria, August 12  18, 2007)
