Fractal random measures generated by time continuous branching and diffusion

Abstract

Fractal measures are often defined in a constructive way. The most of these constructions lead to fractal measures with compact support. In this paper we regard fractal random measures with not necessarily compact support as limits of measure valued processes generated by time continuous branching and diffusion. For the special case of time transformed symmetric Γ-stable motions the almost sure existence of the carrying dimension is proved and an explicit formula for its computation is derived

Keywords:

• Random measures
• Hausdorff dimension
• stable processes
• 1991 Mathematics Subject Classification: Primary 28A80
• Secondary 5811, 60G57

^*Supported by the Deutsche Forschungsgemeinschaft Bonn (DFG)

^*Supported by the Deutsche Forschungsgemeinschaft Bonn (DFG)

Notes

^*Supported by the Deutsche Forschungsgemeinschaft Bonn (DFG)