Almost sure exponential stability of numerical solutions for stochastic delay differential equations

Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the Borel–Cantelli lemma

Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method

Delay-dependent exponential stability of neutral stochastic delay systems

This paper studies stability of neutral stochastic delay systems by linear matrix inequality (LMI) approach. Delay dependent criterion for exponential stability is presented and numerical examples are conducted to verify the effectiveness of the proposed method

Convergence of Monte Carlo simulations involving the mean-reverting square root process

The mean-reverting square root process is a stochastic differential equation (SDE) that has found considerable use as a model for volatility, interest rate, and other financial quantities. The equation has no general, explicit solution, although its transition density can be characterized. For valuing path-dependent options under this model, it is typically quicker and simpler to simulate the SDE directly than to compute with the exact transition density. Because the diffusion coefficient does not satisfy a global Lipschitz condition, there is currently a lack of theory to justify such simulations. We begin by showing that a natural Euler-Maruyama discretization provides qualitatively correct approximations to the first and second moments. We then derive explicitly computable bounds on the strong (pathwise) error over finite time intervals. These bounds imply strong convergence in the limit of the timestep tending to zero. The strong convergence result can be used to justify the method within Monte Carlo simulations that compute the expected payoff of financial products. We spell this out for a bond with interest rate given by the mean-reverting square root process, and for an up-and-out barrier option with asset price governed by the mean-reverting square root process. We also prove convergence for European and up-and-out barrier options under Heston's stochastic volatility model - here the mean-reverting square root process feeds into the asset price dynamics as the squared volatility

Approximate solutions of stochastic differential delay equations with Markovian switching

Our main aim is to develop the existence theory for the solutions to stochastic differential delay equations with Markovian switching (SDDEwMSs) and to establish the convergence theory for the Euler-Maruyama approximate solutions under the local Lipschitz condition. As an application, our results are used to discuss a stochastic delay population system with Markovian switching

Gravitational lensing effects on sub-millimetre galaxy counts

We study the effects on the number counts of sub-millimetre galaxies due to gravitational lensing. We explore the effects on the magnification cross section due to halo density profiles, ellipticity and cosmological parameter (the power-spectrum normalisation $\sigma_8$). We show that the ellipticity does not strongly affect the magnification cross section in gravitational lensing while the halo radial profiles do. Since the baryonic cooling effect is stronger in galaxies than clusters, galactic haloes are more concentrated. In light of this, a new scenario of two halo population model is explored where galaxies are modeled as a singular isothermal sphere profile and clusters as a Navarro, Frenk and White (NFW) profile. We find the transition mass between the two has modest effects on the lensing probability. The cosmological parameter $\sigma_8$ alters the abundance of haloes and therefore affects our results. Compared with other methods, our model is simpler and more realistic. The conclusions of previous works is confirm that gravitational lensing is a natural explanation for the number count excess at the bright end.Comment: 10 pages, 10 figures, accepted by MNRA

A Fast DOA Estimation Algorithm Based on Polarization MUSIC

A fast DOA estimation algorithm developed from MUSIC, which also benefits from the processing of the signals' polarization information, is presented. Besides performance enhancement in precision and resolution, the proposed algorithm can be exerted on various forms of polarization sensitive arrays, without specific requirement on the array's pattern. Depending on the continuity property of the space spectrum, a huge amount of computation incurred in the calculation of 4-D space spectrum is averted. Performance and computation complexity analysis of the proposed algorithm is discussed and the simulation results are presented. Compared with conventional MUSIC, it is indicated that the proposed algorithm has considerable advantage in aspects of precision and resolution, with a low computation complexity proportional to a conventional 2-D MUSIC

Two particle correlations: a probe of the LHC QCD medium

The properties of $\gamma$--jet pairs emitted in heavy-ion collisions provide an accurate mean to perform a tomographic measurement of the medium created in the collision through the study of the medium modified jet properties. The idea is to measure the distribution of hadrons emitted on the opposite side of the %oppositely by tagging the direct photon. The feasibility of such measurements is studied by applying the approach on the simulation data, we have demonstrated that this method allows us to measure, with a good approximation, both the jet fragmentation and the back-to-back azimuthal alignment of the direct photon and the jet. Comparing these two observables measured in pp collisions with the ones measured in AA collisions reveals the modifications induced by the medium on the jet structure and consequently allows us to infer the medium properties. In this contribution, we discuss a first attempt of such measurements applied to real proton-proton data from the ALICE experiment.Comment: 4 pages, 4 figures, Proceedings for Hot Quark 2010 Conferenc

Noise from spatial heterogeneity changes signal amplification magnitude and increases the variability in dose responses

In most molecular level simulations, spatial heterogeneity is neglected by the well-mixed condition assumption. However, the signals of biomolecular networks are affected from both time and space, which are responsible for diverse physiological responses. To account the spatial heterogeneity in the kinetic model, we consider multiple subvolumes of a reaction, introduce parameters representing transfer of ligands between the volumes, and reduce this to an error-term representing the difference between the well-mixed condition and the actual spatial factors. The error-term approach allows modelling of varying spatial heterogeneity without increasing computational burden exponentially. The effect of varying this term, d, between 0 (well-mixed) and 1 (no mixing) and of adding noise to the kinetic constants was then investigated and correlated with knowledge of the behaviour of real systems and situations where network models are inadequate. The spatial distribution effects on the epidermal growth factor receptor (EGFR) in human mammary epithelial tissue, which is involved in proliferation and tumorigenesis, are studied by introducing noisy kinetic constants. The steady-state of the dose response in the EGFR is strongly affected by spatial fluctuations. The ligand-bound receptor is reduced up to 50% from the response without spatial fluctuations and the variance of the steady-state is increased at least 2-fold from the one for no spatial fluctuations. On the other hand, dynamic properties such as the rising time and overshoot are less sensitive to spatial noise