Jin Feng
Phone 785-864-3764
Email jfeng AT math.ku.edu
My research in recent years has been focused on probability and fluid.
The overall effort is to identify notions of entropy and to understand
the (usually hidden) role that they play in some deterministic PDE
models under various
limiting regimes. I develop and utilize techniques in Markov
processes theory, limit theory in probability, viscosity solution for
Hamilton-Jacobi
equations and optimal control, and theory of optimal mass
transportation.
Broadly speaking, I am interested in probability theory and its
applications to natural and bio-sciences.
Teaching
Representative publications
(upto 2011):
Recent works:
- Hamilton-Jacobi
equations
in space of measures associated with a system of conservation
laws (with Truyen
Nguyen), Journal
of Mathematiques Pures et Appliquees, page 318-390, Vol 97
(2012) A short announcement can be found in Comptes
Rendus
Mathematique Vol 349, Issues 17-18, Pages 973-976,September
2011.
- Optimal
control for a mixed flow of Hamiltonian and gradient type in space of
probability measures (with
Andrzej
Swiech and Atanas Stefanov), In
press, Trans. A.M.S.
- Small time
asumptotics for fast mean-reverting stochastic volatility models (with Jean-Pierre Fouque and Rohini
Kumar), In
Press,
Ann. Applied Probability.
- A singular
1-D Hamilton-Jacobi equation, with applications to large deviation of
diffusions (with Xiaoxue
Deng and Yong Liu), Commun. Math. Sci. Vol 1, Issue 9, page
289-300(2011).
- Short
maturity
asymptotics for a fast mean reverting Heston stochastic
volatility model
(with Martin Forde and Jean-Pierre Fouque), SIAM
Journal on Financial Mathematics, Vol 1, pp 126-141 (2010).
- A
Comparison
principle for Hamilton-Jacobi equations related to
controlled gradient flows in infinite dimensions
(with Markos Katsoulakis), Archive for Rational Mechanic
and Analysis, vol 192, page 275-310, (2009)
- Stochastic
scalar
conservation laws (with David Nualart), Journal of
Functional Analysis, vol 255., page 313-373, (2008).
Some
notes:
- Large Deviation and PDE,
Hiroshima
University, Jan. 2011 and Nanjing University, Dec., 2011 --- slides for lecture one.
- Optimal Controlled PDE and
Hamilton-Jacobi equation in Space of Probability Measures,
Institute of Applied Math., Chinese Academy of Sciences, Dec., 2011 and
Hiroshima University, Jan. 2012 --- lecture one, two, three,
four, five.
Large Deviation for Stochastic Processes
(Jin Feng and Thomas G. Kurtz),
(2006)
AMS (American Mathematical Society) "Mathematical Surveys and Monographs 131" 400+
pages. Errata will be maintained here.