Complex Solutions to Bessel SDEs and SLEs

由半鞅驱动的 Loewner 链与复 Bessel 型随机微分方程

On Loewner chains driven by semimartingales and complex Bessel-type SDEs

本文研究半鞅驱动的前向与后向 Loewner 链，证明其迹存在且简单，并应用于 SKLE、Brown 幂函数驱动及复 Bessel 型 SDE。

On Sdes For Bessel Processes In Low Dimension And Path-dependent Extensions

The Bessel process in low dimension (0 $\le$ $δ$ $\le$ 1) is not an It{ô} process and it is a semimartingale only in the cases $δ$ = 1 and $δ$ = 0. In this paper we first characterize it as the unique solution of an SDE with distributional drift or more precisely its related martingale problem. In a second part, we introduce a suitable notion of path-dependent Bessel processes and we characterize them as solutions of path-dependent SDEs with distributional drift.

On squared Bessel particle systems

We study the existence and uniqueness of SDEs describing squared Bessel particles systems in full generality. We define non-negative and non-colliding squared Bessel particle systems and we study their properties.

平方Bessel SDE复数解的大偏差原理

Large Deviation Principle for complex solution to squared Bessel SDE

本文研究了平方Bessel SDE复数解与Schramm-Loewner演化的联系，证明了当维数参数趋于负无穷时该解的大偏差原理。

A limit theorem for singular stochastic differential equations

We study the weak limits of solutions to SDEs \[dX_n(t)=a_n\bigl(X_n(t)\bigr)\,dt+dW(t),\] where the sequence $\{a_n\}$ converges in some sense to $(c_- 1\mkern-4.5mu\mathrm{l}_{x<0}+c_+ 1\mkern-4.5mu\mathrm{l}_{x>0})/x+γδ_0$. Here $δ_0$ is the Dirac delta function concentrated at zero. A limit of $\{X_n\}$ may be a Bessel process, a skew Bessel process, or a mixture of Bessel processes.