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 asymmetry in γγ→μ+μ−+neutrinos\bm{\gamma\gamma \to \mu^+\mu^- + neutrinos} with polarized photons

The difference in distributions of $\mu^+$ and $\mu^-$ in reactions $\gamma \gamma \to \mu^+\mu^-+\nu\bar\nu$ and $\gamma \gamma \to W^\pm\mu^\mp +\nu(\bar\nu)$ with polarized photons at $\sqrt{s}>200$ 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

Charge asymmetries in γγ→μ+μ−+νμνˉμ\gamma\gamma \to \mu^+\mu^- + \nu_{\mu} \bar{\nu}_\mu / γγ→W±μ∓+νμ\gamma \gamma \to W^\pm\mu^\mp +\nu_\mu with polarized photons

It is shown that the difference in the distributions of positive ($\mu^+$) and negative charged leptons ($\mu^-$) in reactions $\gamma \gamma \to \mu^+\mu^-+\nu\bar\nu$ and $\gamma \gamma \to W^\pm\mu^\mp +\nu(\bar\nu)$ at $\sqrt{s}>200$ 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

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 $f$-wave and spin-singlet chiral $d$-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 $d$-wave superconductivity emerges slightly away from it. Surprisingly, the chiral $d$-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