Saturday, November 2

 

8:15-9:00 AM

Registration

 

Session Chair: Alejandro Ramírez, NYU Shanghai

9:00-10:00 AM

 

TBA

By Stefano Olla, Université Paris Dauphine

10:00-10:30 AM

Morning Tea Break

10:30-11:30 AM

 

 

 

 

Fukushima Subspaces of Dirichlet forms

By Jiangang Ying, Fudan University

It is known that a regular Dirichlet form corresponds a symmetric Markov process uniquely. It is rarely known how the domain of Dirichlet form plays a role. In this talk we shall raise the problem how a subspace of a Dirichlet form corresponds Markov process under regularity. As examples, we shall introduce some results on Brownian motion and symmetric stable processes.

11:30 AM-12:30 PM

 

 

 

 

Recent progresses on stochastic Zakharov system

By Deng Zhang, Shanghai Jiao Tong University

In this talk we review very recent progresses on stochastic Zakharov systems in dimensions three and four. Zakharov system couples Schroedinger and wave equations, and reaches the energy criticality in dimension four. We will mainly show the global well-posedness below the ground state and the noise regularization effects on blow-up and scattering dynamics. This talk is based on joint works with Sebastian Herr, Michael Roeckner and Martin Spitz.

12:30 PM-2:30 PM

Lunch Break Session

 

Session Chair: Vahagn Nersesyan, NYU Shanghai

2:30-3:30 PM

 

 

 

 

 

 

 

Generalized Ray-Knight theorems: their applications and limitations

By Elena Kosygina, NYU Shanghai & Baruch College, City University of New York

For several classes of self-interacting random walks on the integers, the generalized Ray-Knight theorems serve as the main tool for finding a candidate for a scaling limit and proving the convergence to that limiting process. A natural question is whether theorems are not just a tool but whether, in fact, they uniquely identify the limiting process and, under some mild conditions, imply convergence. Recently, in a joint work with T. Mountford and J. Peterson, we showed that this need not be the case in general, and more information is needed to imply convergence. This negative answer prompted the follow-up question: would the joint generalized Ray-Knight theorems suffice for the task? In our ongoing project, we explore this idea for two classes of self-interacting random walks that were introduced and studied by B. Tóth in 1995-96.

3:30-4:00 PM

Afternoon Tea Break

4:00-4:40 PM

 

 

 

 

 

 

Limit theorems for additive functionals of some self-similar Gaussian processes

By Fangjun Xu, East China Normal University

Under certain mild conditions, limit theorems for additive functionals of some d-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions, sub-fractional Brownian motions and bi-fractional Brownian motions. To prove these results, we use the method of moments and an enhanced chaining argument. The Gaussian processes under consideration are required to satisfy certain strong local nondeterminism property. A tractable sufficient condition for the strong local nondeterminism property is given and it only relays on the covariance functions of the Gaussian processes.