Asymptotic Behavior of Semistable L,vy Exponents and Applications to Fractal Path Properties

作者：Kern Peter^*; Meerschaert Mark M; Xiao Yimin

来源：Journal of Theoretical Probability, 2018, 31(1): 598-617.

DOI：10.1007/s10959-016-0720-6

• Levy exponent
• Operator semistable process
• Semi-selfsimilarity
• Hausdorff dimension
• Packing dimension
• Range
• Graph
• Multiple points
• Recurrence
• Transience

This paper proves sharp bounds on the tails of the L,vy exponent of an operator semistable law on . These bounds are then applied to explicitly compute the Hausdorff and packing dimensions of the range, graph, and other random sets describing the sample paths of the corresponding operator semi-selfsimilar L,vy processes. The proofs are elementary, using only the properties of the L,vy exponent, and certain index formulae.

• 出版日期2018-3