论文标题
限制拖网过程的定理
Limit Theorems for Trawl Processes
论文作者
论文摘要
在这项工作中，我们得出了拖网过程的限制定理。首先，我们研究了离散的拖网过程的部分总和的渐近行为$（x_ {x_ {iΔ_{n}}）_ {i = 0}^{\ lfloor nt \ rfloor-rfloor-rfloor-rfloor-1} $ $nδ_{n} \rightarrowμ\在[0，+\ infty] $中。其次，随着拖网种子的Lévy度量生长到无穷大，我们得出了拖网过程的功能极限定理，并表明限制过程具有高斯移动平均值。
In this work we derive limit theorems for trawl processes. First,we study the asymptotic behaviour of the partial sums of the discretized trawl process $(X_{iΔ_{n}})_{i=0}^{\lfloor nt\rfloor-1}$, under the assumption that as $n\uparrow\infty$, $Δ_{n}\downarrow0$ and $nΔ_{n}\rightarrowμ\in[0,+\infty]$. Second, we derive a functional limit theorem for trawl processes as the Lévy measure of the trawl seed grows to infinity and show that the limiting process has a Gaussian moving average representation.
