Occupation times of discrete-time fractional Brownian motion

Manfred Denker; Xiaofei Zheng

doi:10.1142/S0219493719500096

Occupation times of discrete-time fractional Brownian motion

Manfred Denker, Xiaofei Zheng

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove a conditional local limit theorem for discrete-time fractional Brownian motions (dfBm) with Hurst parameter 3 4 < H < 1. Using results from infinite ergodic theory, it is then shown that the properly scaled occupation time of dfBm converges to a Mittag-Leffler distribution.

Original language	English (US)
Article number	1950009
Journal	Stochastics and Dynamics
Volume	19
Issue number	1
DOIs	https://doi.org/10.1142/S0219493719500096
State	Published - Feb 1 2019

All Science Journal Classification (ASJC) codes

Modeling and Simulation

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title = "Occupation times of discrete-time fractional Brownian motion",

abstract = "We prove a conditional local limit theorem for discrete-time fractional Brownian motions (dfBm) with Hurst parameter 3 4 < H < 1. Using results from infinite ergodic theory, it is then shown that the properly scaled occupation time of dfBm converges to a Mittag-Leffler distribution.",

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AB - We prove a conditional local limit theorem for discrete-time fractional Brownian motions (dfBm) with Hurst parameter 3 4 < H < 1. Using results from infinite ergodic theory, it is then shown that the properly scaled occupation time of dfBm converges to a Mittag-Leffler distribution.

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Occupation times of discrete-time fractional Brownian motion

Abstract

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