3,573 research outputs found
A Numerical Scheme For High-dimensional Backward Stochastic Differential Equation Based On Modified Multi-level Picard Iteration
In this paper, we propose a new kind of numerical scheme for high-dimensional
backward stochastic differential equations based on modified multi-level Picard
iteration. The proposed scheme is very similar to the original multi-level
Picard iteration but it differs on underlying Monte-Carlo sample generation and
enables an improvement in the sense of complexity. We prove the explicit error
estimates for the case where the generator does not depend on control variate
A generalized scheme for BSDEs based on derivative approximation and its error estimates
In this paper we propose a generalized numerical scheme for backward
stochastic differential equations(BSDEs). The scheme is based on approximation
of derivatives via Lagrange interpolation. By changing the distribution of
sample points used for interpolation, one can get various numerical schemes
with different stability and convergence order. We present a condition for the
distribution of sample points to guarantee the convergence of the scheme.Comment: 11 pages, 1 table. arXiv admin note: text overlap with
arXiv:1808.0156
Stochastic Gronwall's inequality in random time horizon and its application to BSDE
In this paper, we introduce and prove a stochastic Gronwall's inequality in
(unbounded) random time horizon. As an application, we prove a comparison
theorem for backward stochastic differential equation (BSDE for short) with
random terminal time under stochastic monotonicity condition
Representation of Solutions of Linear Homogeneous Caputo Fractional Differential Equations with Continuous Variable Coefficients
We consider the canonical fundamental systems of solutions of linear
homogeneous Caputo fractional differential equations with continuous variable
coefficients. Here we gained a series-representation of the canonical
fundamental system by coefficients of the considered equations and the
representation of solution to initial value problems using the canonical
fundamental system. According to our results, the canonical fundamental system
of solutions to linear homogeneous differential equation with Caputo fractional
derivatives and continuous variable coefficients has different representations
according to the distributions of the lowest order of the fractional
derivatives in the equation and the distance from the highest order to its
adjacent order of the fractional derivatives in the equation.Comment: 22 page
Charge asymmetries in / with polarized photons
It is shown that the difference in the distributions of positive ()
and negative charged leptons () in reactions and at
GeV leads to observable {\em charge asymmetry} of muons which is
sensitive to New Physics effects.Comment: Talk presented by I. F. Ginzburg at Photon 2003: International
Conference on the Structure and Interactions of the Photon and 15th
International Workshop on Photon-Photon Collisions, Frascati, Italy, 7-11 Apr
200
Charge asymmetry in with polarized photons
The difference in distributions of and in reactions and with polarized photons at GeV is a large
observable effect which is sensitive to New Physics phenomena.Comment: 4 pages, talk presented by I. F. Ginzburg at LCWS04, International
Conference on Linear Collider, 19-23 April 2004, Paris, France, to appear in
the Proceeding
Observation of the prior earthquake effect on the flux of environmental neutrons, gamma-radiation, and on the local electric field in Tien Shan mountain
A search for the possible precursors of an earthquake and its effect on the
data series of diverse geophysical parameters has been made in the mountain of
Northern Tien Shan. The complex installation included the NM64 type neutron
supermonitor, detectors of the environmental low-energy neutrons, the
scintillation gamma-detector, the sensor of the local electric field, a
seismograph, and a weather-station. The specialized data filtration methodic
was elaborated with an enhanced sensitivity to the transient signals of seismic
origin. On the eve of, and after a 5.4 magnitude earthquake the fine features
in temporal behavior of the intensity of low-energy neutron and gamma-radiation
background, so as irregularities of the local electric field were observed
which seem to be in a close correlation with each other. These results may be
an evidence of the possibility of experimental identification of earthquake's
precursors in the time up to 2-3 days before the beginning of a period of
intensive tectonic activity
Effect of exchange interaction on electronic instabilities in the honeycomb lattice: A functional renormalization group study
The impact of local and nonlocal density-density interactions on the
electronic instabilities in the honeycomb lattice is widely investigated. Some
early studies proposed the emergence of interaction-induced topologically
nontrivial phases, but recently, it was denied in several works including
renormalization group calculations with refined momentum resolution. We use the
truncated unity functional renormalization group to study the many-body
instabilities of electrons on the half-filled honeycomb lattice, focusing on
the effect of the exchange interaction. We show that varying the
next-nearest-neighbor repulsion and nearest-neighbor exchange integral can lead
to diverse ordered phases, namely, the quantum spin Hall, the spin-Kekul\'e,
and some spin- and charge-density-wave phases. The quantum spin Hall phase can
be induced by a combination of the ferromagnetic exchange and pair hopping
interactions. Another exotic phase, the spin-Kekul\'e phase, develops in a very
small region of the parameter space considered. We encounter the
three-sublattice charge-density-wave phase in a large part of the parameter
space. It is replaced by the incommensurate charge density wave when increasing
the exchange integral. In order to reduce the computational effort, we derive
the explicit symmetry relations for the bosonic propagators of the effective
interaction and propose a linear-response-based approach for identifying the
form factor of order parameter. Their efficiencies are confirmed by numerical
calculations in our work.Comment: 13 pages, 6 figures, 1 Tabl
Estimate of sizes of small asteroids (cosmic bodies) by the method of stroboscopic radiolocation
Radiolocation methods of probing minor celestial bodies (asteroids) by the
nanosecond pulses can be used for monitoring of near-Earth space with the
purpose of identification of hazardous cosmic objects able to impact the Earth.
Development of the methods that allow to improve accuracy of determining the
asteroids size (i.e. whether it measures tens or hundreds meters in diameter)
is important for correctly estimating the degree of damage which they can cause
(either regional or global catastrophes, respectively). In this paper we
suggest a novel method of estimating the sizes of the passive cosmic objects
using the radiolocation probing by ultra-high-resolution nanosecond signals to
obtain radar signatures. The modulation envelope of the reflected signal, which
is a radar portrait of the cosmic object, is subjected to time scale
transformation to carrier Doppler frequency by means of radioimpulse strobing.
The shift of a strobe within the probing period will be performed by radial
motion of the object which will allow to forgo the special autoshift circuit
used in the oscillographic technical equipment. The measured values of duration
of radiolocation portrait can be used to estimate the mean radius of the object
by using the average spatial length of the portrait. The method makes it
possible to appraise the sizes of cosmic objects through their radiolocation
portrait duration, with accuracy that is independent of the objects range
Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling
Motivated by recent discovery of correlated insulating and superconducting
behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice
doped close to the van Hove singularity, using the truncated unity functional
renormalization group approach. We consider an extended Hubbard model on the
honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions,
and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By
varying the strength of the nearest-neighbor exchange coupling and Coulomb
repulsion as free parameters, we present rich ground-state phase diagrams which
contain the spin-triplet -wave and spin-singlet chiral -wave
superconducting phases, the commensurate and incommensurate spin- and
charge-density-wave phases, and the ferromagnetic phase. In the absence of the
exchange coupling and for small value of the nearest-neighbor repulsion, the
four-sublattice spin-density-wave phase is generated right around the van Hove
filling, while the chiral -wave superconductivity emerges slightly away from
it. Surprisingly, the chiral -wave superconductivity is strongly suppressed
by weak nearest-neighbor exchange coupling in our calculations. We argue that
this suppression might be one of the reasons why the chiral superconductivity
proposed for doped graphene has not yet been observed experimentally.Comment: 20 pages, 11 figures, 2 table
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