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Jason Swanson Assistant Professor University of Central Florida Department of Mathematics 4000 Central Florida Blvd P.O. Box 161364 Orlando, FL 32816-1364 Office: MAP 202E Phone: (407) 823-0148 Fax: (407) 823-6253 Email: swanson@mail.singularity.ucf.edu (Remove the singularity.) |
I received my B.S. in 1998, M.S. in 2003, and Ph.D. in 2004, all in mathematics, and all from the University of Washington in Seattle, WA. I was a VIGRE Van Vleck Visiting Assistant Professor at the University of Wisconsin-Madison from 2004--2007. My research area is probability theory, and my primary interests currently include stochastic differential equations, stochastic partial differential equations, interacting particle systems, weak convergence theorems for stochastic processes, Brownian motion, fractional Brownian motion, and financial mathematics.
Curriculum
Vitae (pdf)
Updated August 24, 2010
Homepage for MAC 2311 Calc I
Homepage for MAA 5228
Analysis I
International
Congress of Mathematicians, Hyderabad, India (Aug 19-27,
2010)
4th
International Conference on Stochastic Analysis and Its Applications,
Kansai Univeristy, Osaka, Japan (Aug 30-Sep 3, 2010)
34th
Conference on Stochastic Processes and Their Applications,
Osaka, Japan (Sep 6-10, 2010)
Frontier Probability Days, University of Utah (Mar 10-12, 2011)
Careers in Mathematics
The Best and Worst Jobs in the U.S.
Student Careers
Mathematics-Related Professions
Why Major In Mathematics?
Occupational Outlook Handbook, 2010-11 Edition: Mathematicians
Peter
Donnelly on YouTube (Title: How juries are fooled by
statistics)
Randy
Pausch Lecture: Time Management
The Probability Web
MathOverflow
Wolfram|Alpha
The
weak Stratonovich integral with respect to fractional Brownian motion
with Hurst parameter 1/6
(with Ivan
Nourdin and Anthony
Réveillac)
[arXiv:1006.4238v1]
Fluctuations
of the empirical quantiles of independent Brownian motions
[arXiv:0812.4102]
Crowding
of Brownian spheres (pdf)
(with Krzysztof
Burdzy and Soumik Pal)
ALEA Lat. Am. J. Probab.
Math. Stat., 7:192–205, 2010. link:
http://alea.impa.br/english/index_v7.htm
[arXiv:1002.1057]
A
change of variable formula with Itô correction term
(pdf)
(with Krzysztof
Burdzy)
Ann. Probab.,
38(5):1817–1869, 2010. link:
http://dx.doi.org/10.1214/09-AOP523
[arXiv:0802.3356]
Asymptotic
behavior of a generalized TCP congestion avoidance algorithm (pdf)
(with Teunis J. Ott)
J. Appl. Probab.,
44(3):618–635, 2007. link: http://dx.doi.org/10.1239/jap/1189717533
[arXiv:math/0608476]
Variations
of the
solution to a stochastic heat equation (pdf)
Ann. Probab.,
35(6):2122–2159, 2007.
link:
http://dx.doi.org/10.1214/009117907000000196
[arXiv:math/0601007]
Weak
convergence of the scaled median of independent Brownian motions
(pdf)
Probab. Theory Related
Fields, 138(1-2):269–304, 2007. link: http://dx.doi.org/10.1007/s00440-006-0024-3
[arXiv:math/0507524]
Stationarity
of some processes in transport protocols (pdf)
(with Teunis J. Ott)
SIGMETRICS Perform.
Eval. Rev., 34(3):30–32, 2006. link: http://dx.doi.org/10.1145/1215956.1215969
Variations
of stochastic processes: alternative approaches (pdf)
My doctoral dissertation.
An
introduction to the proof of
Fermat’s last theorem (pdf)
My undergraduate honors thesis. Supervised by Ralph Greenberg.
Fluctuations of the empirical quantiles of independent
Brownian motions
A
change of variable formula with Itô correction term
Malliavin Calculus
in Rd
Conditional expectation
(for professionals)
Conditional
densities, mass functions, and expectations (for
undergraduates)
Transfinite induction
The Feynman-Kac
representation
The expectation of
a product of Gaussian random variables
Lemmas for the
Skorohod space
On the variance of pure jump processes
Supplemental theorems for the Wick product approach to SPDEs
Elementary limit theorems in probability
Game theory and
poker
Randomness in science
The penny game