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- W2962830636 abstract "This work looks at the box-counting dimension of sets related to subordinators (non-decreasing Levy processes). It was recently shown in Savov (Electron Commun Probab 19:1–10, 2014) that almost surely $$lim _{delta rightarrow 0}U(delta )N(t,delta ) = t$$ , where $$N(t,delta )$$ is the minimal number of boxes of size at most $$ delta $$ needed to cover a subordinator’s range up to time t, and $$U(delta )$$ is the subordinator’s renewal function. Our main result is a central limit theorem (CLT) for $$N(t,delta )$$ , complementing and refining work in Savov (2014). Box-counting dimension is defined in terms of $$N(t,delta )$$ , but for subordinators we prove that it can also be defined using a new process obtained by shortening the original subordinator’s jumps of size greater than $$delta $$ . This new process can be manipulated with remarkable ease in comparison with $$N(t,delta )$$ , and allows better understanding of the box-counting dimension of a subordinator’s range in terms of its Levy measure, improving upon Savov (2014, Corollary 1). Further, we shall prove corresponding CLT and almost sure convergence results for the new process." @default.
- W2962830636 created "2019-07-30" @default.
- W2962830636 creator A5080849027 @default.
- W2962830636 date "2018-02-14" @default.
- W2962830636 modified "2023-09-24" @default.
- W2962830636 title "Fractal-Dimensional Properties of Subordinators" @default.
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- W2962830636 doi "https://doi.org/10.1007/s10959-018-0813-5" @default.
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