���ηֲ�������ͳ������

本文研究如何用次序统计量来刻划几何分布, 证明了如下两个命题: (1) 若存在$k,\;1     

�η��������˶���֧��������ŷʽ��Ȩ����

In this paper, we establish the option pricing model under sub-fractional Brownian motion, and consider the situation of the continuous dividend payments. Firstly, Wick-It^{o} integral and partial differential method are used to get the option price of partial differential equation, and then through variable substitution into Cauchy problem, we can get the pricing formula of European call option with dividend-paying in sub-fractional Brownian motion environment.According to the pricing formula of European call option, the European put option pricing formula is obtained. Moreover, we study the parameter estimation in the model, and consider the unbiasedness and the strong convergence of the estimator.     

�η��������˶������ֲ�ʱ�Ĺ⻬��

Let, be two independent,
-dimensional sub-fractional Brownian motions with respective indices.
Assume. Our principal results are the necessary and sufficient condition for the
existence and smoothness of the collision local time and the intersection local time of
and through chaos expansion and elementary inequalities.     

η-INVARIANT AND CHERN-SIMONS CURRENT

The author presents an alternate proof of the Bismut-Zhang localization formula of ηinvariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined ηinvariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.     

η-Invariant and Flat Vector Bundles

Abstract We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to (not necessary unitary) flat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah, Patodi and Singer. * Project supported by the Cheung-Kong Scholarship of the Ministry of Education of China and the 973 Project of the Ministry of Science and Technology of China. (Dedicated to the memory of Shiing-Shen Chern)     

η-Invariant and Flat Vector Bundles

We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to (not necessary unitary) flat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah, Patodi and Singer.     

ξ -η等式的证明方法

介绍了证明ξ-η等式的各种常见方法.     

ȱʧ������varphi����������ηDz����ع麯���ľ�����Ȼ�ƶ�

在φ混合的随机误差下,本文研究了固定设计及响应变量有缺失的非参数回归模型中回归函数的经验似然置信区间的构造.首先采用非参数回归填补法对缺失的数据进行填补,其次利用补足后得到的"完全样本"构造了非参数回归函数的经验似然比统计量,并证明了经验似然比统计量的极限分布为卡方分布,利用此结果可以构造非参数回归函数的经验似然置信区间.     

������Erlang(2)����ģ���µĶ�ηֺ�����

In this paper, an Erlang(2) risk model with time-dependent claims is studied under a multi-layer dividend strategy. First, some piecewise integro-differential equations with certain boundary conditions for the Gerber-Shiu function are derived. Then, applying these results, some defective renewal equations and explicit expressions for the Gerber-Shiu function are obtained when the joint density of the inter-claim time and claim size belongs to the rational family.     

Least squares X=±Xη* solutions to split quaternion matrix equation AXAη*=B

In the paper, the split quaternion matrix equation AXA^η*=B is considered, where the operator A^η* is the η-conjugate transpose of A, where η∈{i,j,k}. We propose some new real representations, which well exploited the special structures of the original matrices. By using this method, we obtain the necessary and sufficient conditions for AXA^η*=B to have X=±X^η* solutions and derive the general expressions of solutions when it is consistent. In addition, we also derive the general expressions of the least squares X=±X^η* solutions to it in case that this matrix equation is not consistent.     

Smoothness of Densities of Generalized Locally Non-Degenerate Wiener Functionals

Several criteria for existence of smooth densities of Wiener functionals are known in the framework of Malliavin calculus. In this article, we introduce the notion of generalized locally non-degenerate Wiener functionals and prove that they possess smooth densities. The result presented here unifies the earlier works by Shigekawa and Florit-Nualart. As an application, we prove that the law of the strong solution to a stochastic differential equation driven by Brownian motion admits a smooth density without an assumption of Lipschitz continuity for dispersion coefficients.     

On the asymptotic relation between equilibrium density and exit measure in the exit problem

In this paper we show that the solution of an anticipating stochastic differential equation with smooth coefficients and with a random and smooth initial condition possesses an infinitely differentiable density under some non-degeneracy conditions     

倒向随机微分方程解的光滑性

该文讨论了倒向随机微分方程Y_t=ξ+∫^T_t{g(s,Y_s,Z_s)}ds-∫^T_t{Z_s}dW_s 解在Malliavin微分意义下的光滑性.对任意的n讨论其解在Malliavin 意义下n 阶可微性,并且证明它是一个线性倒向随机微分方程的解,从而说明BSDE解的光滑性.     

带Poisson 跳跃的正倒向随机延迟系统递归最优控制问题的最大值原理

本文研究了带Poisson 跳跃的正倒向随机延迟系统的递归最优控制问题. 利用经典的针状变分方法、对偶技术和带Poisson 跳跃的超前倒向随机微分方程的相关结果, 证明了最优控制的最大值原理, 包括了最优控制满足的必要条件和充分条件.     

Strong convergence rate of truncated Euler-Maruyama method for stochastic differential delay equations with Poisson jumps

We study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are investigated under the generalized Khasminskii-type condition.     

Iteration of the Lent Particle Method for Existence of Smooth Densities of Poisson Functionals

In previous works (Bouleau and Denis, J Funct Anal 257:1144–1174, 2009, Probab Theory Relat Fields, 2011) we have introduced a new method called the lent particle method which is an efficient tool to establish existence of densities for Poisson functionals. We now go further and iterate this method in order to prove smoothness of densities. More precisely, we construct Sobolev spaces of any order and prove a Malliavin-type criterion of existence of smooth density. We apply this approach to SDE’s driven by Poisson random measures and also present some non-trivial examples to which our method applies.     

Malliavin calculus for infinite-dimensional systems with additive noise

We consider an infinite-dimensional dynamical system with polynomial nonlinearity and additive noise given by a finite number of Wiener processes. By studying how randomness is spread by the dynamics, we develop in this setting a partial counterpart of Hörmander's classical theory of Hypoelliptic operators. We study the distributions of finite-dimensional projections of the solutions and give conditions that provide existence and smoothness of densities of these distributions with respect to the Lebesgue measure. We also apply our results to concrete SPDEs such as a Stochastic Reaction Diffusion Equation and the Stochastic 2D Navier-Stokes System.