68 citations · 89 across the 5 of their papers we have counts for
5 papers
On a Hamilton-Jacobi PDE theory for hydrodynamic limit of action minimizing collective dynamics
Jin Feng
We establish multi-scale convergence theory for a class of Hamilton-Jacobi PDEs in space of probability measures. They arise from context of hydrodynamic limit of N-particle determ…
A system of Schrödinger's problems and functional equations
Toshio Mikami, Jin Feng
We propose and study a system of Schrödinger's problems and functional equations in probability theory. More precisely, we consider a system of variational problems of relative ent…
A Hamilton-Jacobi PDE associated with hydrodynamic fluctuations from a nonlinear diffusion equation
Jin Feng, Toshio Mikami, Johannes Zimmer
We study a class of Hamilton-Jacobi partial differential equations in the space of probability measures. In the first part of this paper, we prove comparison principles (implying u…
Small-time asymptotics for fast mean-reverting stochastic volatility models
Jin Feng, Jean-Pierre Fouque, Rohini Kumar
In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The…
Large deviation for diffusions and Hamilton--Jacobi equation in Hilbert spaces
Jin Feng
Large deviation for Markov processes can be studied by Hamilton--Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to gene…