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 $\lambda(x)$. 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 $\lambda$. One of the possible limits is a skew Brownian motion.

中文翻译：

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时变维纳过程的渐近行为和泛函极限定理

我们研究了适当归一化的时间变化维纳过程的渐近行为。时间变化反映了我们考虑拉普拉斯算子（产生维纳过程）乘以可能退化的状态空间相关强度 $\lambda(x)$ 的事实。将泛函极限定理应用于随机过程的叠加，我们证明了归一化时变维纳过程的泛函极限定理。归一化取决于强度函数 $\lambda$ 的渐近行为。可能的限制之一是偏斜布朗运动。