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arXiv · 1803.01702

Factional Brownian motion with multivariate time in a large convex area: persistence exponents

G. Molchan
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Abstract

The fractional Brownian motion of index $0 < H < 1$, H-FBM, with d-dimensional time is considered on an expanding set TG, where G is a bounded convex domain that contains 0 at its boundary. The main result: if 0 is a point of smoothness of the boundary, then the log-asymptotics of probability that H-FBM does not exceed a fixed positive level in TG is $(H - d + o(1)) \log T$, $T\to\infty$. Some generalizations of this result to isotropic but not self-similar Gaussian processes with stationary increments are also considered.

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G. Molchan. 2018-03-05. Factional Brownian motion with multivariate time in a large convex area: persistence exponents. https://arxiv.org/abs/1803.01702

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