First Passage Problems in Anomalous Diffusion

Rosso, Alberto; Zoia, Andrea

doi:10.1142/9789814590297_0003

Cited by 3 publications

(1 citation statement)

References 49 publications

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“…This paper is concerned with the persistence exponent of a certain class of anomalous diffusion processes. Anomalous diffusion processes are an important tool in modelling physical systems [BG90,MK00,RZ14]. The persistence probability of a real-valued process (X t ) t≥0 is given by…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Persistence Probabilities and Exponents

Аурзада

Simon

2015

Lecture Notes in Mathematics

119

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We consider the persistence probability of a certain fractional Gaussian process 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 exists and is continuous in the Hurst parameter H.Further, the asymptotic behaviour of the persistence exponent for H ↓ 0 and H ↑ 1, respectively, is studied. Finally, for 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 vanishes.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Persistence Probabilities and Exponents

Аурзада

Simon

2015

Lecture Notes in Mathematics

119

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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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Global warming precipitation accumulation increases above the current-climate cutoff scale

Neelin

Sahany

Stechmann

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Precipitation accumulations, integrated over rainfall events, can be affected by both intensity and duration of the storm event. Thus, although precipitation intensity is widely projected to increase under global warming, a clear framework for predicting accumulation changes has been lacking, despite the importance of accumulations for societal impacts. Theory for changes in the probability density function (pdf) of precipitation accumulations is presented with an evaluation of these changes in global climate model simulations. We show that a simple set of conditions implies roughly exponential increases in the frequency of the very largest accumulations above a physical cutoff scale, increasing with event size. The pdf exhibits an approximately power-law range where probability density drops slowly with each order of magnitude size increase, up to a cutoff at large accumulations that limits the largest events experienced in current climate. The theory predicts that the cutoff scale, controlled by the interplay of moisture convergence variance and precipitation loss, tends to increase under global warming. Thus, precisely the large accumulations above the cutoff that are currently rare will exhibit increases in the warmer climate as this cutoff is extended. This indeed occurs in the full climate model, with a 3 • C end-of-century global-average warming yielding regional increases of hundreds of percent to >1,000% in the probability density of the largest accumulations that have historical precedents. The probabilities of unprecedented accumulations are also consistent with the extension of the cutoff.precipitation accumulation | global warming | extreme events | stochastic modeling | first-passage process O ccurrences of intense precipitation are projected to increase (1-8) associated with higher atmospheric moisture content (9, 10) under global warming. Measures of precipitation intensity, coarse-grained to 1-to 5-d intervals, exhibit end-of-century increases on the order of 20% for wettest annual 5-d rainfall (8) or 10% in average wet-day intensity (11) or 17%• C in the 99.9th to 99.999th percentiles of daily precipitation (12) in businessas-usual anthropogenic forcing scenarios. Associated with this, substantial increases in frequency of high-rain-rate events can occur (13-15), and the return times of events exceeding a given threshold decrease (16).Time-integrated accumulation, the amount of precipitation that falls during a single event, is of concern for many societal impacts (17). Because more intense precipitation could, in principle, yield shorter event durations (10), the expected change in accumulation probabilities is unclear. Here, we derive a stochastic prototype from a fundamental climate model equation. This leads to an explanation of key properties of the probability density function (pdf) of accumulations noted in station observations (18-20)-why the pdf of accumulation size drops slowly with increasing size over many orders of magnitude before reaching a cutoff scale, after which the pdf drops...

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First Passage Problems in Anomalous Diffusion

Cited by 3 publications

References 49 publications

Persistence Probabilities and Exponents

Persistence Probabilities and Exponents

Persistence Probabilities of a Smooth Self-Similar Anomalous Diffusion Process

Global warming precipitation accumulation increases above the current-climate cutoff scale

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