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Some fractal properties of the image measure of an $$\alpha$$-stable process. (Chinese. English summary) Zbl 0964.60047
Summary: Let $$X(t)$$, $$t\in \mathbb{R}^+$$, be an $$\alpha$$-stable process on $$\mathbb{R}^d$$ ($$0<\alpha\leq 2$$, $$\alpha\neq 1$$) and $$\mu$$ be a finite positive Borel measure. We discuss the fractal properties of the imague measure $$\mu_X$$, get the upper and lower Hausdorff dimension of $$\mu_X$$, and we use the dimension of $$\mu$$ to give a condition such that $$\mu_X$$ is absolutely continuous with respect to $$\lambda_d$$ (the Lebesgue measure on $$\mathbb{R}^d$$).
##### MSC:
 60G17 Sample path properties 28A78 Hausdorff and packing measures 60G52 Stable stochastic processes