时间均匀扩散的Engelbert-Schmidt型零一律的新证明

Engelbert–Schmidt条件下的一维Feynman–Kac正则性

One-dimensional Feynman--Kac regularity under the Engelbert--Schmidt conditions

该研究针对系数满足Engelbert–Schmidt条件的时齐一维扩散过程，证明了Feynman–Kac半群的正则性，指出连续性足以保证内部$C^{1,2}$正则性，并通过实例说明结论在二维情形不成立。

关于瞬态随机游动范数过程的一个零一律

On a zero-one law for the norm process of transient random walk

证明了瞬态随机游动的范数过程的Engelbert-Schmidt型零一律。随机游动局部时间的不变原理和Jeulin引理的极限版本起着关键作用。

具有积分准则的一维扩散问题的最优停止

Optimal stopping of one-dimensional diffusions with integral criteria

本文利用积分准则给出了一维扩散最优停止问题的值函数和解的充分刻画。结果在很弱的假设下成立，即假设扩散是满足Engelbert-Schmidt条件的随机微分方程的弱解，而（随机）贴现率和被积函数只需要满足一般的可积性条件.

Path transformations for local times of one-dimensional diffusions

Let $X$ be a regular one-dimensional transient diffusion and $L^y$ be its local time at $y$. The stochastic differential equation (SDE) whose solution corresponds to the process $X$ conditioned on $[L^y_{\infty}=a]$ for a given $a\geq 0$ is constructed and a new path decomposition result for transient diffusions is given. In the course of the construction of the SDE the concept of {\em recurrent transformation} is introduced and {\em Bessel-type motions} as well as their SDE representations are studied. A remarkable link between an $h$-transform with a minimal excessive function and recurrent …

基于时齐扩散的随机波动率模型的鞅性

On the martingale property in stochastic volatility models based on time-homogeneous diffusions

Lions和Musiela（2007）给出了证明连续局部鞅的随机指数是鞅或一致可积鞅的充分条件。Blei和Engelbert（2009）和Mijatović和Urusov（2012 c）给出了完全相关（ρ=1）的充要条件。对于金融应用，如检验相关随机波动率模型中股票价格过程的鞅性，我们将他们的工作推广到任意相关情形（-1<=ρ<=1）.我们给出了时间齐次扩散的积分泛函的收敛性质的一个完整分类，并推广了Mijatović和Urusov（2012 b）（2012 c）的结果，并提供了避免使用分离时间的替代证明（Cherny和Urusov（2004）引入的概念，并广泛用于Mijatović和Urusov（2012 c）的证明）。

Hilbert--Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations

Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates are of the form of Hilbert--Schmidt norms of the integral operator and its square root, composed with fractional powers of an elliptic operator equipped with homogeneous boundary conditions of either Dirichlet or Neumann type. These types of estimates, which couple the regularity of the driving noise with the properties of the differential operator, have imp…