论文标题
无限时间地平线布朗尼桥的当地时间
Local time of infinite time horizon Brownian bridge
论文作者
论文摘要
我们引入了一个无限的时间范围布朗桥，该桥由随机的兰格文（Langevin）方程确定，并依赖于时间依赖漂移系数。我们表明，当时间到达无穷大并研究其当地时间以及其时间变量的Hölder连续性的存在和渐近行为时，这个过程几乎肯定会零。主要困难是该过程缺乏平稳性，因此不适用静态（高斯）过程的强大工具。我们采用Garsia-Rodemich-Rumsey不平等，解决这种困难。
We introduce an infinite time horizon Brownian bridge which is determined by a stochastic Langevin equation with time dependent drift coefficient. We show that this process goes to zero almost surely when the time goes to infinity and study the existence and asymptotic behavior of its local time as well as its Hölder continuity in time variable and in location variable. The main difficulty is the lack of stationarity of the process so that the powerful tools for stationary (Gaussian) processes are not applicable. We employ the Garsia-Rodemich-Rumsey inequality to get around this type of difficulty.
