2nd International
Conference on
Stochastic
Analysis and Its
Applications
May 28-31, 2008 at Seoul National
University, Seoul, Korea
Title and
Abstract of Talks
Rodrigo Bañuelos, Purdue University,
USA
Title : Finite dimensional distributions.
Abstract : We will discuss how many interesting properties of various
spectral theoretic objects for the Laplacian, the fractional Laplacian,
and other Lévy operators, reduce to properties of finite
dimensional distributions (multiple integrals) which can then be
studied by elementary means.
Krzysztof Bogdan, Wroclaw University of
Technology,
Poland
Title : Schrödinger perturbations of transition densities
Abstract : Under a condition of conditional smallness of
time-inhomogeneous
Schrödinger perturbations with respect to an arbitrarily given
transition density, the perturbed transition density is shown to be
comparable. Explicit estimates and applications are given. A joint work
with Tomasz Jakubowski and Wolfhard Hansen.
Zhen-Qing Chen, University of Washington,
USA
Title : Stationary distributions for diffusions with inert drift
Abstract : Consider a reflecting diffusion in a domain in R^d that
acquires drift
in proportion to the amount of local time spent on the boundary of the
domain. We show that the stationary distribution for the joint law of
the position of the reflecting
process and the value of the drift vector has a product form. Moreover,
the first component is the symmetrizing measure on the domain for the
reflecting diffusion without inert drift, and the second component has
a Gaussian distribution. We also consider processes where the drift is
given in terms of the gradient of a potential.
Joint work with R. Bass, K. Burdzy and M. Hairer
HyeongIn Choi, Seoul National
University, Korea
Title : Approximate HJM Term Structure Model with Jump
Abstract : A finite dimensional multi-factor HJM term structure model
with jump is
introduced. In this model the evolution of the forward curve is
confined to a predetermined finite dimensional linear function space --
for example, a space spanned by finite number of orthogonal
polynomials. The risk neutrality condition is expressed in terms of
minimization problem in the function space. When examined with the
actual U.S. Treasury Bond data of the past ten years, we found that 4
or 5 orthogonal polynomials give very satisfactory result in terms of
bond error even in the present of jumps: namely, the maximum error
compared with the usual HJM is typically less than 1 bp. One advantages
of this model is that it is very easy to fit any correlation matrix,
which was not easily done in practice with the term structure models
devised so far. Other advantage of this model is its linear
nature that makes it better amenable to many linear techniques like
regression analysis and etc. This model can also be profitably
used in the stress test situation in the market risk management system.
Masatoshi Fukushima, Osaka University,
Japan
Title : On unique extension of a time changed transient reflecting
Brownian motion
Abstract :
Fuzhou Gong, Chinese Academy of Sciences,
China
Title : Log-Sobolev Inequalities on Metric Spaces
Abstract : Inspired by Yann Ollivier's recent work, we prove a
standard logarithmic Sobolev inequality for any random walk on a Polish
space with positive Ricci curvature. We also discuss relative problems
for resistance forms and give some examples such as the Sierpinski
gasket and carpet.
Qingyang Guan, Loughborough University,
UK
Title : Boundary Harnack inequality of regional fractional Laplacian
Abstract:
We talk on boundary Harnack inequalities of regional fractional
Laplacians which are generators of a class of stable-like processes on
open sets. These boundary Harnack inequalities were first proved for
the homogeneous case by Bogdan, Burdzy and Chen.
Tomasz Grzywny,
Wroclaw University of Technology,
Poland
Title : Intrinsic ultracontractivity for symmetric Levy processes
Abstract:
Masanori Hino, Kyoto University, Japan
Title : Sets of finite perimeter and Hausdorff measures on the
Wiener
space
Abstract : According to the geometric measure theory on the
Euclidian space, the
integration by parts formula for a set of finite perimeter is expressed
by way of the surface measure that is provided by the 1-codimensional
Hausdorff measure on the reduced boundary.
In this talk, we discuss its counterpart for the abstract Wiener space
and give a representation of the surface measure by the Hausdorff
measure on some suitable set that may be smaller than the topological
boundary.
Niels Jacob, University of Wales Swansea, UK
Title : A Theorem of Schoenberg, an Observation of P.A.Meyer, and
Dirichlet Forms Related to Certain Symmetric Levy Processes
Abstract : The theorem of Scoenberg in our mind is the one
characterizing metric
spaces which can be isometrically embedded into Hilbert spaces.
Implicitly this is behind an observation of P.A.Meyer on how to
represent the carre du champ of a symmetric Levy process as an infinite
sum of squares. For a large class of symmetric Levy processes we give a
direct construction of this representation and will prove en passant
Schoenberg's theorem (in the cases under discussion). Our construction
promises the possibility to develop an "infinite dimensional
differential geometry" associated with these Levy processes,
This is joint work with Victoria Knopova.
Jeong-Han Kim, Yonsei University, Korea
Title : Random Graphs, Random Regular Graphs and Couplings
Abstract : The study of random regular graphs, started in late 70's,
has recently
attracted much attention.
Main questions in this area have been whether the random regular graph
contains a perfect matching, a Hamilton cycle, and a Hamilton
decomposition. These properties are closely related to the contiguity
of random models. Roughly speaking, two models are contiguous if they
are essentially the same. For example, one may consider the uniform
random 3-regular graph and the union of three independent random
perfect matchings, and ask whether the two models are essentially the
same or not. We will discuss contiguity of various random regular graph
models.
We will also introduce some attempts to study random (hyper)graphs by
means of random regular (hyper)graphs. In particular, we will discuss
recent improved bounds for Shamir's problem regarding when the random
uniform hypergraph contains a perfect matching.
Kyeong-Hun Kim, Korea
University, Korea
Title : L_p theory of Stochastic Partial Differential Equations
Abstract : SPDEs are equations having stochastic noises in the
equations. Those
are used, for instance, to describe natural phenomena which can't be
modeled by deterministic equations due to incomplete knowledge,
uncertainity in the measurments or existence of
randomness in the phenomena. For instance, Stochastic
Navier-Stokes Equation is used to describe the motion of a fluid with
random external forces.
In this talk, we present the unique solvability of 2nd order parabolic
SPDEs in Sobolev spaces.
Takashi Kumagai,
Kyoto University, Japan
Title : Uniqueness of Brownian motion on Sierpinski carpets
Abstract : We prove that, up to scalar multiples, there exists only one
Dirichlet
form on a generalized Sierpinski carpet that is invariant with respect
to the local symmetries of the carpet.
Consequently for each such fractal the law of Brownian motion is
uniquely determined and the notion of Laplacian is well defined, which
has been a long open problem in this area. This is a
joint work with M.T. Barlow, R.F. Bass and A. Teplyaev.
Kazuhiro Kuwae,
Kumamoto University, Japan
Title : On double Feller property
Abstract : We investigate the double Feller property of each
transformed semigroup
of Feynman-Kac or Girsanov type under the double Feller property of the
semigroup of Markov processes. This is a joint work with ZhenQing Chen.
Mateusz Kwasnicki, Wroclaw University of Technology,
Poland
Title : Intrinsic ultracontractivity for isotropic stable processes in
unbounded domains.
Abstract :
Zhi-Ming Ma, Chinese Academy of Sciences, China
Title : On the Structure of Non-symmetric Dirichlet forms
Abstract : I shall report our results on the structure of non-symmetric
Dirichlet
forms. The talk is based on several joint papers of Zechun Hu, Zhi-Ming
Ma and Wei Sun. Our research in this direction has been conducted for
several years. Very recently we obtain some significant progress which
leads to, among other things, a complete characterization of
non-symmetric Dirichlet forms on R^d . The topics of my talk will
include the Beurling-Deny formula for semi-Dirichlet forms, LeJan's
transformation rule for non-symmetric Dirichlet forms on Lusin
mesurable spaces, and Lévy-Khintchine formula for non-symmetric
Dirichlet forms on R^d.
Jacek Malecki, Wroclaw University of Technology,
Poland
Title : Bessel Potentials, Hitting Distributions, and Green
Functions
Abstract :
Michal Ryznar, Wroclaw University of Technology,
Poland
René Schilling, TU Dresden, Germany
Title : Stochastic Processes and their Symbols
Abstract : Many Feller processes are generated by pseudo differential
operators
having negative definite symbols. We give a brief survey on this topic
and then move on to discuss to which class of processes one can
associate a symbol. We will then use the symbols to derive various path
properties of the processes under consideration.
Yuichi Shiozawa, Ritsumeikan University, Japan
Title : Central limit theorem for branching Brownian motions in
random
environment
Abstract : We consider a branching Brownian motion in space-time random
environment associated with the Poisson random measure. When the
randomness of the environment is moderated by that of the Brownian
motion, we prove that the population density satisfies a central limit
theorem and that the growth rate of the population is the same as its
expectation with strictly positive probability. We also study the decay
rate for the density at the most populated site and for the replica
overlap. On the other hand, when the randomness of the environment
dominates, we show that the growth rate of the population is strictly
less than its expectation almost surely, in connection with Brownian
directed polymers in random environment introduced by Comets and
Yoshida.
Renming Song, University of Illinois, USA
Title : Heat kernel estimates for killed stable processes and
censored
stable processes
Abstract : In this talk I will present recent results on two-sided
sharp estimates
on the heat kernel of killed stable processes and censored stable
processes. This talk is based on some recent papers with Z.-Q. Chen and
Panki Kim.
Jason Swanson, University of Central
Florida, USA
Title : A change of variable formula with Itô correction term
Abstract:
Pawel Sztonyk, TU Dresden, Germany
Title : Estimates of tempered stable densities
Abstract : Estimates of densities of convolution semigroups of
probability
measures are given under specific assumptions on the corresponding Levy
measure and the Levy--Khinchin exponent. The assumptions are satisfied,
e.g., by tempered stable semigroups of J. Rosinski.
Byron Schmuland, University of Alberta, Canada
Title : Reversible Fleming-Viot processes
Abstract : What forces the mutation operator of a reversible
Fleming-Viot process
to be uniform? Our explanation is based on Handa's result that
reversible distributions must be quasi-invariant under a certain flow,
making the mutation operator satisfy a cocycle identity.
We also apply these ideas to a system of interacting Fleming-Viot
processes as defined and studied by Dawson, Greven, and Vaillancourt.
Masayoshi Takeda, Tohoku University, Japan
Gerald Trutnau, University of Bielefeld, Germany
Title : A remark on the generator of a right-continuous Markov
process
Abstract :
Toshihiro Uemura, University of Hyogo, Japan
Zoran Vondraček, University of Zagreb,
Croatia
Title : Two results on subordinate Brownian motion
Abstract :
Tusheng Zhang, University of Manchester,
UK
Title : SPDEs with reflection: strong Feller properties and Harnack
inequalities.
Abstract : In this talk, I will present some recent results on strong
Feller
properties and Harnack inequalities for solutions of SPDEs with
reflection. As an application of the Harnack inequality, a Varadhan
type small time symptotics will also be discussed.
Xiaowen Zhou, Concordia University, Canada
Title: The exit problem of a partially reflected spectrally
negative
Levy process.
Abstract : This talk concerns a stochastic process obtained by
partially
reflecting a spectrally negative Levy process from its running maximum.
Applying the excursion theory we want to study the one-sided and
two-sided exit problems for such a process. We will derive expressions
for solutions to the exit problems. We will also point out its possible
applications in actuarial mathematics.