Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve

Cox-Ingersoll-Ross过程和具有可访问边界的Bessel过程的强收敛性及时间正则性

Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundaries

本文研究了CIR过程和Bessel过程在可访问边界下的强收敛性及时间正则性，提出了一种隐式平方根欧拉方法，并证明其在L^p距离下的强收敛性。

Exact Simulation of Bessel Diffusions

We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change of measure. All these diffusions are broadly used in mathematical finance for modelling asset prices, market indices, and interest rates. We show how the probability distributions of a squared Bessel bridge and a squared Bessel process with or withou…

Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes

The Bessel process with parameter $D>1$ and the Dyson model of interacting Brownian motions with coupling constant $β>0$ are extended to the processes in which the drift term and the interaction terms are given by the logarithmic derivatives of Jacobi's theta functions. They are called the elliptic Bessel process, eBES$^{(D)}$, and the elliptic Dyson model, eDYS$^{(β)}$, respectively. Both are realized on the circumference of a circle $[0, 2 πr)$ with radius $r >0$ as temporally inhomogeneous processes defined in a finite time interval $[0, t_*), t_* < \infty$. Transformations of them to Schrö…

平方贝塞尔过程的直接反演法及其应用

Direct Inversion for the Squared Bessel Process and Applications

提出基于二维切比雪夫展开的直接反演方法模拟平方贝塞尔过程及非中心卡方变量，解决了小自由度计算难题，并高效应用于CIR过程模拟。

Strong solutions to a beta-Wishart particle system

The purpose of this paper is to study the existence and uniqueness of solutions to a Stochastic Differential Equation (SDE) coming from the eigenvalues of Wishart processes. The coordinates are non-negative, evolve as Cox-Ingersoll-Ross (CIR) processes and repulse each other according to a Coulombian like interaction force. We show the existence of strong and pathwise unique solutions to the system until the first multiple collision, and give a necessary and sufficient condition on the parameters of the SDE for this multiple collision not to occur in finite time.

一维平方Bessel过程的最优强逼近

Optimal Strong Approximation of the One-dimensional Squared {B}essel Process

本文研究了一维平方Bessel过程在终时点的强逼近问题，发现自适应算法和等距网格算法的收敛率分别为无穷大和1/2，表明自适应方法显著提高了收敛速度。

相互作用扩散的交换机制：框架、与切换的比较及一个精确可解示例

The Swapping Mechanism for Interacting Diffusions: Framework, Comparison with Switching, and an Exactly Solvable Example

研究两个相互作用跳跃扩散过程的交换机制，开发严格框架，建立相关性质，通过对称恒等式联系交换与状态切换，对比两者差异，给出精确可解示例并分析其性质，揭示不对称性、扩散率修正及收敛率等。