4,981 research outputs found
Harnack Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion
For stochastic differential equation driven by fractional Brownian motion
with Hurst parameter , Harnack type inequalities are established by
constructing a coupling with unbounded time-dependent drift. These inequalities
are applied to the study of existence and uniqueness of invariant measure for a
discrete Markov semigroup constructed in terms of the distribution of the
solution. Furthermore, we show that entropy-cost inequality holds for the
invariant measure
Uniform disconnectedness and Quasi-Assouad Dimension
The uniform disconnectedness is an important invariant property under
bi-Lipschitz mapping, and the Assouad dimension implies the
uniform disconnectedness of . According to quasi-Lipschitz mapping, we
introduce the quasi-Assouad dimension such that
implies its quasi uniform disconnectedness. We obtain and compute the quasi-Assouad dimension
of Moran set
Stochastic gravitational-wave background from spin loss of black holes
Although spinning black holes are shown to be stable in vacuum in general
relativity, there exists exotic mechanisms that can convert the spin energy of
black holes into gravitational waves. Such waves may be very weak in amplitude,
since the spin-down could take a long time, and a direct search may not be
feasible. We propose to search for the stochastic background associated with
the spin-down, and we relate the level of this background to the formation rate
of spinning black holes from the merger of binary black holes, as well as the
energy spectrum of waves emitted by the spin-down process. We argue that
current LIGO-Virgo observations are not inconsistent with the existence of a
spin-down process, as long as it is slow enough. On the other hand, the
background may still exist as long as a moderate fraction of spin energy is
emitted within Hubble time. This stochastic background could be one interesting
target of next generation GW detector network, such as LIGO Voyager, and could
be extracted from total stochastic background
Determining the nature of white dwarfs from low-frequency gravitational waves
An extreme-mass-ratio system composed of a white dwarf (WD) and a massive
black hole can be observed by the low-frequency gravitational wave detectors,
such as the Laser Interferometer Space Antenna (LISA). When the mass of the
black hole is around , the WD will be disrupted by the
tidal interaction at the final inspiraling stage. The event position and time
of the tidal disruption of the WD can be accurately determined by the
gravitational wave signals. Such position and time depend upon the mass of the
black hole and especially on the density of the WD. We present the theory by
using LISA-like gravitational wave detectors, the mass-radius relation and then
the equations of state of WDs could be strictly constrained (accuracy up to
). We also point out that LISA can accurately predict the disruption
time of a WD, and forecast the electromagnetic follow-up of this tidal
disruption event.Comment: 7 pages, 2 figure
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