Persistence probabilities of weighted sums of stationary Gaussian sequences

Аурзада, Франк; Mukherjee, Sumit

doi:10.1016/j.spa.2023.02.003

Stochastic Processes and their Applications

2023

DOI: 10.1016/j.spa.2023.02.003

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Persistence probabilities of weighted sums of stationary Gaussian sequences

Франк Аурзада

Sumit Mukherjee

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2024

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Persistence Probabilities of a Smooth Self-Similar Anomalous Diffusion Process

Aurzada,

Mittenbühler

2024

J Stat Phys

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We consider the persistence probability of a certain fractional Gaussian process $$M^H$$ M H that appears in the Mandelbrot-van Ness representation of fractional Brownian motion. This process is self-similar and smooth. We show that the persistence exponent of $$M^H$$ M H exists, is positive and continuous in the Hurst parameter H. Further, the asymptotic behaviour of the persistence exponent for $$H\downarrow 0$$ H ↓ 0 and $$H\uparrow 1$$ H ↑ 1 , respectively, is studied. Finally, for $$H\rightarrow 1/2$$ H → 1 / 2 , the suitably renormalized process converges to a non-trivial limit with non-vanishing persistence exponent, contrary to the fact that $$M^{1/2}$$ M 1 / 2 vanishes.

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Persistence Probabilities of a Smooth Self-Similar Anomalous Diffusion Process

Aurzada,

Mittenbühler

2024

J Stat Phys

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Persistence probabilities of weighted sums of stationary Gaussian sequences

Cited by 1 publication

References 16 publications

Persistence Probabilities of a Smooth Self-Similar Anomalous Diffusion Process

Persistence Probabilities of a Smooth Self-Similar Anomalous Diffusion Process

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