论文标题
1-D随机粒子的追求问题中的领导指数
Leadership exponent in the pursuit problem for 1-D random particles
论文作者
论文摘要
对于n + 1个颗粒在直线上独立移动的粒子，我们研究了其中一个领先位置可以持续多长时间的问题。我们的重点是概率p（t，n）的渐近学，当N和T大时，领导者时间将超过t。假定粒子的动力学是由独立的，无论是固定还是相似的高斯过程，不一定是相同分布的。粗略地，具有单位方差固定动力学的粒子的结果如下：l = -log p（t，n）/（tlog n）= 1/d+o（1），其中d/（2pi）是领先粒子频谱中零频率的幂，并且该值是该谱的最大值。以前，在某些特定模型中，L的渐近学首先是t之上的顺序极限，然后是n上。对于不一定具有非负相关性的过程，对T的极限可能不存在。为了克服这一困难，在域堵塞中考虑了生长的参数t和n，其中c> 1。 Lamperti变换使我们能够将所描述的结果转移到log P（t，n）的标准器中，成为log t log n。
For n + 1 particles moving independently on a straight line, we study the question of how long the leading position of one of them can last. Our focus is the asymptotics of the probability p(T,n) that the leader time will exceed T when n and T are large. It is assumed that the dynamics of particles are described by independent, either stationary or self-similar, Gaussian processes, not necessarily identically distributed. Roughly, the result for particles with stationary dynamics of unit variance is as follows: L= -log p(T,n) /(Tlog n)=1/d+o(1), where d/(2pi) is the power of the zero frequency in the spectrum of the leading particle, and this value is the largest in the spectrum. Previously, in some particular models, the asymptotics of L was understood as a sequential limit first over T and then over n. For processes that do not necessarily have non-negative correlations, the limit over T may not exist. To overcome this difficulty, the growing parameters T and n are considered in the domain clog T<log n<CT, where c>1 . The Lamperti transform allows us to transfer the described result to self-similar processes with the normalizer of log p(T,n) becoming log T log n.
