Chii-Ruey Hwang

Diffusions for global optimizations

We seek a global minimum of

Diffusion for global optimization in R n

U:[0,1]^n \to R

Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

. The solution to

Singular perturbed Markov chains and exact behaviors of simulated annealing processes

({d / {dt}})x_t = - \nabla U(x_t )

The behavior of the spectral gap under growing drift

will find local minima. The solution to

Discovering stock dynamics through multidimensional volatility phases

dx_t = - \nabla U(x_t )dt + \sqrt {2T} dw_t

A chaos hypothesis for some large systems of random equations

, where w is standard (n-dimensional) Brownian motion and the boundaries are reflecting, will concentrate near the global minima of U, at least when “temperature” T is small: the equilibrium distribution for

Disorder Chaos in the Spherical Mean-Field Model

x_t

On the Optimal Transition Matrix for Markov Chain Monte Carlo Sampling

, is Gibbs with density

A generalization of Chernoff inequality via stochastic analysis

\pi _T (x)\alpha \exp \{ - {{U(x)} / T}\}