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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 September 24, 2008
Calculus and Analytic Geometry I Honors
Calculus and Analytic Geometry III
UCF Probability and Statistics
Seminar
Gaussian
Analysis & Stochastic Partial Differential Equations
(October 2008)
Seminar
on Stochastic Processes (March 2009)
33rd
Conference on Stochastic Processes and Their Applications
(July 2009)
International
Congress of Mathematicians (August 2010)
A
change of variable formula with Itô correction term
(with Krzysztof
Burdzy)
[arXiv:0802.3356]
Variations
of the
solution to a stochastic heat equation (pdf)
Ann. Probab. 35
(2007), no. 6, 2122--2159. link:
http://projecteuclid.org/euclid.aop/1191860418
[arXiv:math.PR/0601007]
Asymptotic
behavior of a generalized TCP congestion avoidance algorithm
(with Teunis J. Ott)
J. Applied Prob.
44 (2007), no. 3, 618--635. link: http://projecteuclid.org/euclid.jap/1189717533
[arXiv:math.PR/0608476]
Weak
convergence of the scaled median of independent Brownian motions
Probab. Theory Related Fields, 138 (2007), Nos. 1-2,
269--304. DOI: http://dx.doi.org/10.1007/s00440-006-0024-3
[arXiv:math.PR/0507524]
Stationarity
of some processes in transport protocols
(with Teunis J. Ott)
SIGMETRICS Perform. Eval. Rev. 34, 3 (Dec. 2006),
30--32. DOI: http://doi.acm.org/10.1145/1215956.1215969
Variations
of stochastic processes: alternative approaches
My doctoral dissertation. [pdf]
An
introduction to the proof of
Fermat’s last theorem
My undergraduate honors thesis. Supervised by Ralph Greenberg. [pdf]
A change of variable formula with Itô correction term
The Sleeping Beauty
problem
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
Game theory and poker
Randomness in science
Supplemental theorems for the Wick product approach to SPDEs
Elementary limit theorems in probability
The penny game