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arXiv · 1011.4807

Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries

Kay Jörg Wiese·Satya N. Majumdar·Alberto Rosso
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Abstract

Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations ~ t^{2H} + s^{2H} - |t-s|^{2H}, where H, with 0 0 (near the absorbing boundary), while R(y) ~ y^gamma exp(-y^2/2) as y -> oo, with phi = 1 - 4 epsilon + O(epsilon^2) and gamma = 1 - 2 epsilon + O(epsilon^2). Our epsilon-expansion result confirms the scaling relation phi = (1-H)/H proposed in Ref. [28]. We verify our findings via numerical simulations for H = 2/3. The tools developed here are versatile, powerful, and adaptable to different situations.

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Kay Jörg Wiese, Satya N. Majumdar, Alberto Rosso. 2011-04-11. Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries. https://doi.org/10.1103/physreve.83.061141

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