Speakers and their titles

Brownian survival and Lifshitz tail in perturbed lattice disorders

Abstract: We consider the annealed asymptotics for the survival probability of Brownian motion among randomly distributed killing potentials. The configuration is given by independent displacements of the lattice points. We determined the asymptotics for the logarithm of the survival probability up to multiplicative constant. As an application, we determined the Lifshitz tail exponents for the density of states of associated random Schr\"{o}dinger operators.

Asymptotic expansion theorem for functionals of a Poisson random measure

Abstract

Weyl type spectral asymptotics for Laplacians on Sierpinski carpets

Abstract

Recurrent and transient sets of time inhomogeneous diffusion processes

Abstract: There are many interesting feature concerning the recurrence or transience of some sets in the time inhomogeneous case because a set can be recurrent or transient depending on the fluctuation of the generator relative to time parameter. In this talk, we consider a time inhomogeneous diffusion process obtained by a time dependent drift transformation from a diffusion process and give general criteria for the recurrence and transience of some sets.

Heat kernel estimates for Dirichlet fractional Laplacian environment

Abstract: In this talk, we discuss the sharp two-sided estimates for the heat kernel of Dirichlet fractional Laplacian in open sets. This heat kernel is also the transition density of a rotationally symmetric $\alpha$-stable process killed upon leaving an open set. Our results are the first sharp two-sided estimates for the Dirichlet heat kernel of a non-local operator on open sets. This is a joint work with Zhen-Qing Chen and Renming Song.

Central limit theorem for a class of linear systems

Abstract: In this talk we consider a class of interacting particle systems of which the binary contact path process is an example. For $d\ge 3$ and a certain condition on parameter we prove a central limit theorem for the density of the particles together with upper bounds for the density of the most populated site and the replica overlap.

A note on localization for branching Brownian motions in random environment

Abstract: We consider a branching Brownian motion in random environment associated with the Poisson random measure in space-time. It is known that, if the randomness of the environment is moderated by that of the Brownian motion, then this process is diffusive. In this talk, we will show that, if the randomness of the environment dominates, then this process has a localization property.

Harmonic transform of one dimensional generalized diffusion processes

Abstract: We consider a one dimensional generalized diffusion opereator ${\mathcal G}$ represented by triplet of Borel measures and its harmonic transform ${\mathcal G}^*_h$. We show that our harmonic transform is an {\it inverse} of $h$-transform treated in paper of Miyuki Maeno (2005) in some sense. We observe a relation between recurrent [resp. transient] property of ${\mathcal G}$ and recurrent [resp. transient] property of ${\mathcal G}^*_h$. We also characterize the state of boundaries for the generalized diffusion process with generator ${\mathcal G}^*_h$ in termes of Borel measures and harmonic function.

Spectral bounds of Shcr\"{o}dinger-type operators with non-local potentials

Abstract: We consider the $L^p$-independence of spectral bounds of Schr\"{o}dinger-type operators with local and non-local potentials. We consider a symmetric jump-diffusion process on a locally compact separable metric space. In this talk, we establish a necessary and sufficient condition for spectral bounds of local and non-local Feynman-Kac semigroup being $L^{p}$-independent.

Large deviation for additive functionals of jump-diffusion processes

Abstract: As a useful approach in proving the large deviation principle, the G\"artner-Ellis theorem is well known. For additive functionals generated by low-dimensional symmetric Markov processes, we can apply the G\"artner-Ellis theorem directly to show the large deviation principle of additive functionals. In this talk, we prove the large deviation principle of additive functionals for high-dimensional symmetric Markov processes with another method. These Markov processes consist of jump and diffusion part. This is a joint work with Zhen-Qing Chen.

On potential theory of one-dimensional subordinate Brownian motion

Abstract: A subordinate Brownian motion $X$ is a Levy process obtained by subordinating a Brownian motion by an independent subordinator. In this talk I am going to discuss how one can use information given by the subordinator to obtain some potential-theoretic results of the process $X$ killed upon exiting the half-line or an interval. The key information, given by the potential density of the ladder height process of $X$, can be deduced form the underlying subordinator. In particular, I will derive the Green function estimate for a sum of Brownian motion and $\alpha$-stable process, and prove the boundary Harnack principle for this process. This is joint work with Panki Kim and Renming Song.

Penalisation of symmetric stable Levy paths with Feynman Kac weights

Abstract: As a continuation of Yuko Yano's talk, we study limit theorems with Feynman Kac weights in the case of symmetric stable Levy processes. We also characterise the class of non-negative martingales which appear as the Radon Nikodym densities of possible limit measures of penalisation problems unified by our sigma-finite measure. The present talk is based on the joint work by K. Yano-Y. Yano-M. Yor.

Penalisation of symmetric stable Levy paths with a function of local time

Abstract: Roynette--Vallois--Yor (RVY) have studied limit theorems of Wiener measure weighed by some classes of positive functionals converging to zero. Najnudel--Roynette--Yor (NRY) have introduced a sigma-finite measure which unifies the limit theorems of RVY. In the present talk, we study limit theorems with a function of local time in the case of symmetric stable Levy processes. We put a special emphasis on a stable Levy counterpart of the sigma-finite measure of NRY. The present talk is based on a joint work with Kouji Yano and Marc Yor.

Calculation of the MEMM for geometric Levy processes and its applicatioin to option pricing

Abstract

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