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
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Publications
Preprints (papers below are available at http://arxiv.org, click on the titles below to see).
1.
E. Nane and Y. Ni. Timechanged Stochastic Control
Problem and its Maximum Principle Theory. Submitted, 2019.
2.
X. Meng and E. Nane. Spacetime fractional stochastic
partial differential equations with Levy noise. Submitted, 2019.
3.
E. Nane, Y. Xiao and
A. Zeleke. Strong laws of large
numbers for arrays of random variables and stable random fields.
Submitted, 2018.
4.
Guerngar, E. Nane and S. Ulusoy. Inverse problem for a threeparameter
spacetime fractional diffusion equation. Submitted, 2018.
5.
S. Asogwa, M. Foodun, J. Mijena and E. Nane. Critical parameters for
reactiondiffusion equations involving spacetime fractional derivatives.
Submitted, 2018.
6.
H. D. Binh, E. Nane, and N.
Huy Tuan. Approximation of mild
solutions of a semilinear fractional elliptic
equation with random noise. Submitted, 2018.
7.
E. Nane and N. Guerngar. Moment bounds of a class of
stochastic heat equations driven by spacetime colored noise in bounded
domains. Submitted, 2018.
8.
E. Nane and N. H. Tuan. Convergence rates in expectation
for a nonlinear backward parabolic equation with Gaussian white noise.
Submitted, 2017.
9.
M. Kirane, E. Nane and N. H. Tuan. Regularized solutions for some
backward nonlinear partial differential equations with statistical data.
Submitted, 2017.
To Appear/In press:
1.
S.Asogwa,
J. B. Mijena and E. Nane. Blowup
results for spacetime fractional stochastic partial differential equations.
Potential Anal., To Appear, 2019.
Publications Starting From
2019
1.
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).
2. 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
1.
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.
2.
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.
3.
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.
4.
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.
5.
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).
6. 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
1.
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.
2.
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.
3.
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.
4.
Y. Ҫenesiz, A. Kurt
and E. Nane. Stochastic
solutions of Conformable fractional Cauchy problems. Statistics & Probability
Letters., Volume 124, May 2017, 126131.
5.
M. Foodun and E. Nane. Asymptotic properties of some spacetime
fractional stochastic equations. Mathematische
Zeitschrift (2017), pp. 127.
doi:10.1007/s0020901618343.
6.
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
1.
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.
2.
E. Nane and Y. Ni. Stochastic Solution of Fractional
FokkerPlanck Equations with SpaceTimeDependent Coefficients. Journal of Mathematical
Analysis and Applications 442 (2016) 103116
3.
M. D`ovidio and
E. Nane. Fractional
Cauchy problems on compact manifolds. Stochastic Analysis and Applications, Vol. 34 (2016), No. 2,
232257.
4.
J.B. Mijena and E. Nane. Intermittence and time fractional
stochastic partial differential equations. Potential Anal. Vol. 44 (2016) 295312.
2015
1. J.B. Mijena and E. Nane. Spacetime fractional stochastic
partial differential equations. Stochastic Process. Appl.
125, (2015) 33013326.
2014
1.
J. B. Mijena and E. Nane. Correlation structure of
timechanged Pearson diffusions. Statistics & Probability
Letters. Volume 90, (2014), 6877.
2.
J. B. Mijena and E. Nane. Strong analytic solutions of
fractional Cauchy problems. Proceedings of the American Mathematical Society,
142 (2014), 17171731.
3.
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.
4.
M. D`ovidio and
E. Nane. Time
dependent random fields on spherical nonhomogeneous surfaces. Stochastic Process. Appl.
124 (2014) 20982131.
2013
1.
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.
2.
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.
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.
10831093.
2012
1.
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.
2.
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).
3.
E. Nane, D. Wu and Y. Xiao. αtime fractional Brownian
motion: PDE Connections and Local Times. ESAIM:P&S,
Vol. 16 (2012), 124.
2011
1.
M.M. Meerschaert,
E. Nane and P. Vellaisamy. Distributedorder fractional diffusions on bounded
domains. Journal of Mathematical
Analysis and Applications. 379 (2011) 216228.
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, 16001620.
3.
Arun Kumar, E. Nane and P. Vellaisamy. Timechanged Poisson processes.
Statistics & Probability
Letters. 81 (2011) 18991910.
2010
1.
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.
2.
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
1.
B. Baeumer, M.M. Meerschaert
and E. Nane. Spacetime
duality for fractional diffusion. Journal of
Applied Probability, Volume
46, Number 4 (2009), 11001115.
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 17441751.
3.
B. Baeumer, M.M. Meerschaert
and E. Nane. Brownian
subordinators and fractional Cauchy problems. Trans. Amer. Math. Soc. 361 (2009),
39153930.
4.
M.M. Meerschaert,
E. Nane and P. Vellaisamy. Fractional Cauchy problems on
bounded domains. The Annals of Probability , Vol. 37,
(2009) No. 3, 9791007
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
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.
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, Çankaya 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, Çankaya 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)
