应用概率与统计研讨会
为了进一步加强概率统计青年学者之间的交流，展示本领域学者的最新
研究成果， 2015 年 10 月 23 日在南京航空航天大学理学院举办“应用
概率与统计研讨会”。此次研讨会由国家自然科学基金项目
（11101210），中央高校基本科研业务费项目（NS2015074）共同支持。
研讨会主要组织者：
蒋辉
（副教授）
日程安排
时间：2015 年 10 月 23 日（周五）
地点：南京航空航天大学理学院五楼 547 室
时间
报告人
主题
王春武副院长
9:00-9:10
(南京航空航天大学理学 研讨会致辞
院)
主持专家：耿显民 教授（南京航空航天大学）
Prof. Hacene Djellout Estimation of the realized
9:10-10:00
(University Blaise
(co-)volatility: large deviation
Pascal, France)
approach
10:00-10:10
茶歇
主持专家：Prof. Hacene Djellout（University Blaise Pascal, France）
王冉(Ran Wang)
Irreducibility of stochastic real
副教授 (Associated
Ginzburg-Landau equation driven by
10:10-11:00
Professor)
$\alpha$-stable noises and
(中国科技大学)
applications
郭旭(Xu Guo)
Model checking for parametric
副教授(Associated
single-index models: A
11:00-11:50
Professor)
dimension-reduction
(南京航空航天大学)
model-adaptive approach
12:00
午餐
主持专家：王冉 副教授（中国科技大学）
14:00-14:50
储为娟(Weijuan Chu)
博士(P.H.D)
(南京大学)
The small value probability and
self-normalized large
deviation for supercritical
branching processes
刘俊峰(Junfeng Liu) 副
On a class of nonlinear fractional
教授(Associated
14:50-15:40
Stochastic partial differential
Professor)
equation
(南京审计学院)
15:40-16:00
茶歇、照相
主持专家：蒋辉 副教授教授（南京航空航天大学）
严钧(Jun Yan)
Deviations and asymptotic behavior
副教授(Associated
of convex and coherent entropic risk
16:00-16:50
Professor)
measures for compound Poisson
(扬州大学)
process influenced by jump times
王绍臣(Shaochen Wang) Asymptotic properties of
16:50-17:40
博士(P.H.D)
eigenvalues and its functionals for
(华南理工大学)
several random matrices models
18:00
晚
餐
报告题目、摘要
Prof. Hacene Djellout
Title: Estimation of the realized (co-)volatility: large deviation
approach
Abstract: Realized statistics based on high frequency returns have become
very popular in financial economics. In recent years, different
non-parametric estimators of the variation of a log-price process have
appeared. These were developed by many authors and were motivated by the
existence of complete records of price data. Among them are the realized
quadratic (co-)variation which is perhaps the most well known example,
providing a consistent estimator of the integrated (co-)volatility when
the logarithmic price process is continuous. Limit results such as the
weak law of large numbers or the central limit theorem have been proved
in different contexts. In this paper, we propose to study the large
deviation properties of realized (co-)volatility (i.e., when the number
of high frequency observations in a fixed time interval increases to
infinity. More specifically, we consider a bivariate model with
synchronous observation schemes and correlated Brownian motions of the
following form:
for
denotes the log-price, we are concerned
with
the
, where
large deviation
estimation of the vector
and
where
represente the estimator of the quadratic variational
processes
and the integrated covariance
respectively, with
. Our main
motivation is to improve upon the existing limit theorems. Our large
deviations results can be used to evaluate and approximate tail
probabilities of realized (co-)volatility. As an application we provide
the large deviation for the standard dependence measures between the two
assets returns such as the realized regression coefficients up to time
$t$, or the realized correlation. Our study should contribute to the
recent trend of research on the (co-)variance estimation problems, which
are quite often discussed in high-frequency financial data analysis.
The jump case will be also considered. This is a joint work with Jiang
Hui, Guillin Arnaud and Samoura Yacouba.
王冉 副教授
Title: Irreducibility of stochastic real Ginzburg-Landau equation driven
by $\alpha$-stable noises and applications
Abstract: We establish the irreducibility of stochastic real
Ginzburg-Landau equation with $\alpha$-stable noises by a maximal
inequality and solving a control problem. As applications, we prove that
the system converges to its equilibrium measure with exponential rate
under a topology stronger than total variation and obeys the moderate
deviation principle by constructing some Lyapunov test functions; we also
establish large deviation principle by Wu's hyper-exponential recurrence
criterion. It is based on joint works with Jie Xiong and Lihu Xu.
郭旭 副教授
Title: Model checking for parametric single-index models: A
dimension-reduction model-adaptive approach
Abstract: Local smoothing testing based on multivariate nonparametric
regression estimation is one of the main model checking methodologies in
the literature. However, the relevant tests suffer from typical
curse of dimensionality, resulting in slow convergence rates to their
limits under the null hypothesis and less deviation from the null
hypothesis under alternative hypotheses. This problem prevents tests from
maintaining the significance level well and makes tests less sensitive
to alternative hypotheses. In this paper, a model-adaptation concept in
lack-of-fit testing is introduced and a dimension-reduction
model-adaptive test procedure is proposed for parametric single-index
models. The test behaves like a local smoothing test, as if the model was
univariate. It is consistent against any global alternative hypothesis
and can detect local alternative hypotheses distinct from the null
hypothesis at a fast rate that existing local smoothing tests can achieve
only when the model is univariate. Simulations are conducted to
examine the performance of our methodology. An analysis of real data is
shown for illustration. The method can be readily extended to global
smoothing methodology and other testing problems.
储为娟 博士
Title: The small value probability and self-normalized large
deviation for supercritical branching processes
Abstract: For the supercritical branching processes, there is a positive,
finite and non-degenerate limit W after suitable normalization. The
limiting behavior of W is an interesting topic. We considered the small
value probability of W, that is the convergence rate of
as x
converges to zero, in the immigration case. Also we applied Shao QiMan(1997)'s result about self-normalized large deviation to obtain the
self-normalizedlarge deviation for supercritical branching processes.
刘俊峰 副教授
Title: On a class of nonlinear fractional Stochastic partial differential
equation
Abstract: In this talk, we will introduce the following fractional
stochastic partial differential equation of the form
where
process,
denotes the Markovian generator of stable-like Feller
is a measurable function, and
is a double parameter fractional noise. We will study the existence,
uniqueness and Holder regularity of the solution. In addition, we prove
the lower and upper Gaussian bounds for the probability density of the
mild solution via Malliavin calculus and the new tool developed by Nourdin
and Viens (Electron. J. Probab. 14(2009)).
严钧 副教授
Title: Deviations and asymptotic behavior of convex and coherent entropic
risk measures for compound Poisson process influenced by jump times
Abstract: In this article, we study several deviations and asymptotic
behavior of convex and coherent entropic risk measures for the compound
Poisson process influenced by jump times. The parameters of the risk
measures under consideration are assumed to depend on time t.
王绍臣 博士
Title: Asymptotic properties of eigenvalues and its functionals for
several random matrices models
Abstract:In this talk, we focus on the asymptotic behaviors
of severlrandom matrices models, especially the sample covaria
nce matrix. Somebasic results of random matrix theory will b
e reviewed first. The Cramer type moderate
deviations and
Berry-Esseen bounds for eigenvaluesand its functionals will be
given for sample covariance matrix. Two applications of
t
hese results will also be presented.
欢迎有兴趣的老师和研究生同学参加！