Abstract
Let $X(t), X(0) = 0$, be a nonsingular diffusion in the natural scale in a neighborhood of 0, and let $\mathbf{f}(t, x)$ be its local time. The local behavior of $X(\mathbf{f}^{-1}(t, 0))$ is studied, and used to obtain upper and lower functions of a new type for $X(t)$ at $t = 0$.
Citation
Frank B. Knight. "Local Variation of Diffusion in Local Time." Ann. Probab. 1 (6) 1026 - 1034, December, 1973. https://doi.org/10.1214/aop/1176996808
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