论文标题
在自我相互作用扩散的出口问题上
On the exit-problem for self-interacting diffusions
论文作者
论文摘要
我们研究了从自我相互作用扩散的域中的退出时间，在该域中，布朗运动被常数$σ$的$σb_t$取代。这项工作的第一部分是表明，先前在\ cite {kk-ejp}中获得的收敛速率（对某些明确的吉布斯度量的职业量度的量度（kk-ejp}）的收敛速率，对于凸{kk-ejp}而言，对于凸限制的潜在$ v $和cONVEX的交互潜力可以均匀地限制在$队标上。然后，我们证明了第一次退出领域的Arrhenius型定律（满足Freidlin-Wentzell理论的经典假设）。
We study the exit-time from a domain of a self-interacting diffusion, where the Brownian motion is replaced by $σB_t$ for a constant $σ$. The first part of this work consists in showing that the rate of convergence (of the occupation measure of the self-interacting process toward some explicit Gibbs measure) previously obtained in \cite{kk-ejp} for a convex confinment potential $V$ and a convex interaction potential can be bounded uniformly with respect to $σ$. Then, we prove an Arrhenius-type law for the first exit-time from a domain (satisfying classical hypotheses of Freidlin-Wentzell theory).
