Jin Feng
Phone 785-864-3764
Email jinfeng AT ku.edu (replace the AT by @ with no space
left in between)
I have been working on the large deviation theory, the
Hamilton-Jacobi equations especially those optimal control of PDEs
associated with mass transport problems, nonlinear PDEs associated
with random behavior. My most recent focus is in understanding the
metric analysis nature of singularities in a number of variational
PDEs associated with infinite particle mechanics and statistical
mechanics.
I am currently interested in two lines of works: A) The first
principled approach in understanding large deterministic systems in
relation with probability (very hard). B) a more
pragmatic approach by effectively model things
probabilistically, and then develop mathematical theories
associated with these models (e.g. stochastic PDEs, large
deviations, optimal transport ...).
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A book:
Some publications after moving to
Kansas:
In the past several
years, I have been working on a new notion of viscosity solution for
very singular Hamilton-Jacobi equations that includes the example of
infinitely many deterministic Newtonian particles interacting
through the mean-field. I will post a final version here once it is
fully ready.
- On a
class of first order Hamilton-Jacobi equations in metric
spaces (with
Luigi Ambrosio), Journal of Differential Equations, Vol 256, Issue
7, 2194-2245 (2014).
- Optimal control for a mixed flow
of Hamiltonian and gradient type in space of probability
measures (with
Andrzej Swiech and Atanas Stefanov), Trans.
A.M.S. Vol 365, 3987-4039 (2013).
- 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 in Comptes
Rendus
Mathematique
Vol
349,
Issues
17-18,
Pages
973-976,
September
2011.
- Small time
asumptotics for fast mean-reverting stochastic volatility
models (with
Jean-Pierre Fouque and Rohini Kumar), Ann.
Applied Probability, Vol 22, No.4, 1541-1575
(2012).
- A singular 1-D Hamilton-Jacobi
equation, with applications to large deviation of diffusions (with
Xiaoxue Deng and Yong Liu), Commun. Math. Sci. Vol 9, No. 1,
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).