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Contact
information
E-mail: nane@auburn.edu
Phone: 334 844-6595
Fax: 334-844-6555
Teaching (Spring Semester, 2013)
MATH 1627 Honors Calculus II
(MTWF 08:00-08:50am. 328 Parker Hall)
MATH 7830: Applied Stochastic Processes II(MWF
9:00-9:50am. 246 Parker Hall)
International
Year of Statistics
The Year of Mathematics of
Planet Earth
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.
Two-term
trace estimates for relativistic stable processes: (Joint with Rodrigo Bañuelos, and Jebessa Mijena). Submitted. (PDF file)
2.
Time dependent
random fields on spherical non-homogeneous surfaces: (Joint with Mirko D’ovidio). Submitted.
To Appear/In press:
.
1.
J. Mijena and E. Nane. Strong analytic solutions of
fractional Cauchy problems.
(To appear) Proceedings of the American Mathematical Society.
Publications Starting From
2013
1.
E. Nane and Hassan Allouba. 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
motion, Electron.
J. Probab. 11 (2006), no. 18, 434—459.
6.
CTRW Limits: Fractal
Properties and Governing Equations. 8th
World Congress in Probability and Statistics. Istanbul, Turkey
(July 9-14, 2012).
7.
Continuous
Time Random Walk Limits: Governing Equations and Fractal Dimensions.
Probability Colloquium, Department of Mathematics,
Selcuk University, Konya, Turkey (July 2012)
8.
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.
9.
Continuous Time Random Walk Limits:
Governing Equations and Fractal Dimensions. Colloquium, Department
of Mathematical Sciences, University of Alabama at Huntsville (Nov 2011).
10.
Time-Changed Processes and Cauchy Problems. Colloquium, Department of Mtahematics, University of Alabama at Birmingham,
Birmingham, Al (September 2011).
11.
Fractional Cauchy Problems for time-changed Processes.
Tufts University Probability Seminar, Boston, MA (February 2011).
12.
Cauchy Problems Solved by Running Subordinate Processes.
Informs 2010 Annual meeting. Austin,
Texas (November 7-10, 2010)
13.
Cauchy Problems in Bounded Domains and Iterated
Processes. EMS2010, 28th European Meeting of
Statisticians. EMS 2010, Piraeus,
Greece, University of Piraeus (August 2010).
14.
Fractional Cauchy problems
on bounded domains: survey of recent results. Third Conference on Nonlinear Science and
Complexity. Ankara, Turkey, Çankaya
University (July 2010).
15.
Domain of Attraction for stochastic processes,
Probability Seminar, Auburn University, October 2008.
16.
Fractional Cauchy Problems,
Gaussian Analysis &
SPDEs (October
2008), University Of Alabama in Huntsville, AMS Souteastern
sectional meeting.
17.
Subordinated processes and Cauchy problems, Malliavin Calculus & Appl. Regional CBMS/NSF conference, Kent State University,
OHIO, August 6-12, 2008.
18.
Subordinated processes and Cauchy problems,
Probability Seminar, Department of mathematics, University of Illinois,
Urbana-Champaign, April 2008.
19.
Iterated Brownian motion and a related class of
processes. Department of Mathematics Colloquium,
University of Oregon, Eugene, Oregon, February 2008.
20.
Iterated
Brownian motion and a related class of processes. Department of Mathematics
and Statistics Colloquium, Auburn
University, Alabama, February 2008.
21.
Iterated Brownian motion and a related class of
processes. Department of Mathematics and Statistics Colloquium,
American University, Washington, DC, February
2008.
22.
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.
23.
Symmetric α-stable
subordinators and Cauchy problems. Fourth International Conference of Applied
Mathematics and Computing, (Plovdiv, Bulgaria, August 12 - 18,
2007). Some references.
24.
Symmetric α-stable
subordinators and Cauchy problems. Department of Statistics and
Probability Seminar, Michigan State
University, March 2007. (two-hour lecture). Some references.
25.
Iterated Brownian motion:
lifetime asymptotics and isoperimetric-type
inequalities, Department of Statistics and Probability Colloquium, Michigan State University, September 2006. Some references.
26.
Iterated Brownian motion in open sets in Rn, Probability Seminar at the Purdue
University, October 2004.
Related Conferences
27.
8th World
Congress in Probability and Statistics. Istanbul, Turkey (July
9-14, 2012).
28.
NSF/CBMS Regional Research
Conference in the Mathematical Sciences. University of Alabama in
Huntsville, AL, June 4--8, 2012.
29.
4th International Conference on Porous Media &
Annual Meeting of the International Society for Porous Media. Purdue
University, West Lafayette, IN, May 14-16, 2012.
30.
Informs 2010 Annual meeting. Austin,
Texas (November 7-10, 2010)
31.
EMS2010, 28th European Meeting of
Statisticians. EMS 2010, Piraeus,
Greece, University of Piraeus (August 2010).
32.
Third Conference on Nonlinear Science and Complexity.
Ankara, Turkey, Çankaya University (July 2010).
33.
Gaussian
Analysis & SPDEs (October 2008)
34.
Malliavin Calculus & Appl. (August 2008)
35.
Twenty
Ninth Midwest Probability Colloquium at the Northwestern University, October 19--20, 2007.
36.
Fourth International
Conference of Applied Mathematics and Computing, (Plovdiv,
Bulgaria, August 12 - 18, 2007)
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