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In this paper, the theory of Malliavin
derivative has been applied to explore the solution $(y,z)$ of
BSDEs. First a method of comparing part $z$ has been got via the
Malliavin derivative of part $y$. As an application of this method,
comonotonic theorems of BSDEs, which consist of stochastic
generators, have been obtained.
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Stochastic differential equations with
random impulses should have extensive applications. In this paper,
the existence and uniqueness in mean square of solutions to these
equations are considered. To achieve the desired results, many
techniques are used, such as Pearson iteration, the Cauchy-Schwarz
inequality, Lipschitz conditions, Ito isometry, martingale
inequality and some stochastic analysis.
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Phylogenetics studies the evolutionary relationships
between species. The nucleotide substitution models in phylogenetics
usually assume that evolutions of sequences have neither missing nor
censored, which is hard to be satisfied in fact. Facing to the fact
above, we use an EM algorithm to estimate parameters, to construct a
fine phylogenetic tree of the sequences which have the same length
after deletions and insertions. Main points of this paper is to
estimate best parameters of DNA sequences having censored data for
Jukes-Cantor Model and Kimura Model under the conditions of rooted
tree and unrooted tree respectively.
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Multivariate $t$ distributions belong to
elliptically contoured distributions. However, they are symmetric.
In many fields such as economics, psychology and sociology,
sometimes error structures in a regression type models no longer
satisfy symmetric property. Generally there is a presence of high
skewness. Therefore, multivariate skew elliptical distributions have
been developed. In this paper, properties about known family of
multivariate skew $t$ distributions are stressed. Linear
transformations, marginal and conditional density are given. Also
moments are derived.
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Processes of Ornstein-Uhlenbeck type, driven
by positive compound Poisson processes, are considered in this
paper. We are interested in parametric estimation of those processes
based on discrete observations. The parameter of the stationary
distribution is estimated by the method of moments, and a consistent
and asymptotically normal estimator is provided. The theoretical
study is also generalized to the superposition case.}
\newcommand{\fundinfo}{The research is supported by the National Natural
Science Foundation of China (10901100) and the Science \& Technology
Program of Shanghai Maritime University (20100135).
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In the paper, a global solution is guaranteed
under local Lipschitz condition and some additional conditions
without linear growth condition. Later, the convergence in
probability of approximate solutions is investigated on the neutral
stochastic differential delay equations with Poisson jumps and
Markovian switching, instead of $L^{2}$. Some known results are
generalized and improved.
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In this paper, we consider the semiparametric
mixed-effects model under longitudinal data. We use kernel weight
function method and moment method to construct the estimators of
fixed effects and individual effects. Asymptotic normality of the
estimators are investigated, and the confidence region of the
estimators of fixed effects is constructed. The simulations are
reported for illustration, and the results are encouraging.
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The estimator of expectation of interval
censored data can be established by means of unbiased
transformations. In this paper, we go further to study the variances
of these estimators. In interval-censored Case 1 and
interval-censored Case 2, when the tail of the density function of
the censoring variable is thicker than that of the density function
of the censored variable to some extent, the estimators with finite
variance can be easily obtained.
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In this paper, we consider the varying-coefficient
errors-in-variables regression model. The local bias-corrected
empirical log-likelihood ratio statistic for the unknown coefficient
function is proposed. It is shown that the proposed statistic has
the asymptotic chi-square distribution under some suitable
conditions, and hence it can be used to construct the pointwise
confidence regions of the coefficient functions. A simulation study
is carried out to compare the performance of the empirical
likelihood and the normal approximation method based on the
pointwise confidence regions.
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This paper discusses the prediction
of time series. Without the assumptions on the traditional
time series models, this paper considers all the indicators
by balancing different types of forecasting models, so that
the turning point in the time series can be found. An example
of stock time series is given to show the effectiveness of
the predictive model provided.
