Limit Theorems for Local and Occupation Times of Random Walks and Brownian Motion on a Spider

Csáki, Endre; Csörgő, Miklós; Földes, Antónia; Révész, Pál

doi:10.1007/s10959-017-0788-7

Cited by 4 publications

(1 citation statement)

References 36 publications

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“…Further potential applications may be found in the research on the most favorite sites of a stochastic process, see Bass and Griffin [3], Shi and Toth [22] and references therein. In fact, our interest in the problem was arisen by Endre Csáki and Antonia Földes who in [8] together with Csögö and Révész studied local times of BM on a multiray (also called a spider).…”

Section: Introductionmentioning

confidence: 99%

On the local time process of a skew Brownian motion

Borodin

Salminen

2019

Trans. Amer. Math. Soc.

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We derive a Ray-Knight type theorem for the local time process (in the space variable) of a skew Brownian motion up to an independent exponential time. It is known that the local time seen as a density of the occupation measure and taken with respect to the Lebesgue measure has a discontinuity at the skew point (in our case at zero), but the local time taken with respect to the speed measure is continuous. In this paper we discuss this discrepancy by characterizing the dynamics of the local time process in both these cases. The Ray-Knight type theorem is applied to study integral functionals of the local time process of the skew Brownian motion. In particular, we determine the distribution of the maximum of the local time process up to a fixed time, which can be seen as the main new result of the paper.

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Section: Introductionmentioning

confidence: 99%