论文标题
渐近行为和功能极限定理一段时间改变了维纳过程
Asymptotic behaviour and functional limit theorems for a time changed Wiener process
论文作者
论文摘要
我们研究了正确归一化的时间的渐近行为改变了维纳过程。时间变化反映了一个事实，即我们认为拉普拉斯操作员（生成维纳过程）乘以可能退化的状态空间依赖性强度$λ（x）$。在随机过程的叠加中，应用功能极限定理，我们证明了归一化时间变化的Wiener过程的功能极限定理。归一化取决于强度函数$λ$的渐近行为。可能的限制之一是偏斜的布朗尼运动。
We study the asymptotic behaviour of a properly normalized time changed Wiener processes. The time change reflects the fact that we consider the Laplace operator (which generates a Wiener process) multiplied by a possibly degenerate state-space dependent intensity $λ(x)$. Applying a functional limit theorem for the superposition of stochastic processes, we prove functional limit theorems for the normalized time changed Wiener process. The normalization depends on the asymptotic behaviour of the intensity function $λ$. One of the possible limits is a skew Brownian motion.
