论文标题
几乎是周期性的固定过程
Almost periodic stationary processes
论文作者
论文摘要
我们为随机过程提供了几乎有限的尺寸分布的必要条件；特别是，我们获得了无限划分过程的特征，从其特征性三胞胎几乎是周期性的。此外，我们得出条件，当过程$（x_t）_ {t \ in \ r} $由随机积分$ x_t定义$ x_t：= \ int _ {\ r^d} f（t，t，s）dl（s）dl（s）$几乎是周期性的，并且几乎是周期性的，也几乎是周期性的。 l^1（\ r^d，\ r）\ cap l^2（\ r^d，\ r）$是确定性的，$ l $是lévy的基础。此外，我们讨论了几乎周期性的Ornstein-Uhlenbeck-type过程，并获得了$ m $依赖性过程的中心限制定理，这些过程几乎是周期性的有限尺寸分布。
We derive a necessary and sufficient condition for stochastic processes to have almost periodic finite dimensional distributions; in particular, we obtain characterizations for infinitely divisible processes to be almost periodic in terms of their characteristic triplets. Furthermore, we derive conditions when the process $(X_t)_{t\in\R}$ defined by the stochastic integral $X_t:= \int_{\R^d} f(t,s) dL(s)$ is almost periodic stationary and also when it is almost periodic in probability, where $f(t,\cdot)\in L^1(\R^d,\R)\cap L^2(\R^d,\R)$ is deterministic and $L$ is a Lévy basis. Moreover, we discuss almost periodic Ornstein-Uhlenbeck-type processes, and obtain a central limit theorem for $m$-dependent processes with almost periodic finite dimensional distributions.
