Electric field generation by the electron beam filamentation instability: Filament size effects

The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their nonrelativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated, that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small contribution of the thermal pressure gradient to the force balance implied, that the electrostatic field performed undamped oscillations around a background electric field. Here we consider larger filaments, which reach a stronger electrostatic potential when they saturate. The electron heating is enhanced and electrostatic electron phase space holes form. The competition of several smaller filaments, which grow simultaneously with the large filament, also perturbs the balance between the electrostatic and magnetic fields. The oscillations are damped but the final electric field amplitude is still determined by the MPGF.Comment: 14 pages, 10 plots, accepted for publication in Physica Script

Chaos-Order Transition in Matrix Theory

Classical dynamics in SU(2) Matrix theory is investigated. A classical chaos-order transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum large enough the system is regular.Comment: 14 pages, Latex, 10 figure

The explicit form of no arbitrage condition when the term structure model is multi-factor

The no arbitrage conditions are derived in the explicit form for the market, where the zero coupons bonds of various maturities are accessible for the investors to draw up the portfolios. It is supposed, that the investor at any moment of time has a possibility to make the self-financed portfolio of given value. It is considered that the processes of the short interest rate and rates of inflation follow the stochastic differential equations. The known result for a portfolio with two assets is extended on case of any number of assets and inflation. The no arbitrage condition for multi-factor models of a term structure of the interest rates is considered. The condition of existence of a risk free self-financed portfolio is obtained at first, and then for want of it fulfillment the no arbitrage condition is derived

The Processes with Dependent Increments as Mathematical Models of the Interest Rate Processes

Processes of the interest rates and other financial indexes in continuous time are usually modeled in the literature by stochastic processes with independent increments. Such processes are described by the stochastic differential equations and are the Markov processes. As it follows from the theory the stationary stochastic process is the Markov process (in the wide sense) if and only if the normalized correlation function is exponential. In other words the stochastic processes with independent increments generate the data series with the exponential correlation functions. At the same time the correlation functions of real data series have often non-exponential correlation functions. For example such functions are typical for the US Treasury Security Yield Rate, Internal Rate of Yield on UK 2.5 % Consols, UK Dividend Yield Rate for Shares and other financial data series. Therefore in order that to fit a mathematical model to some real financial data it should be used a stochastic processes with dependent increments. Such processes have more flexible structure that allows obtain the necessary properties. In present paper it is proposed a way for the construction of the process with dependent increments. For that it is supposed that the stochastic process of the interest rate (or other financial index) has a derivative of the some order and this derivative is the process with independent increments. In other words the stochastic process of the interest rate is described by the stochastic differential equation of some order more than first. It results in the more relevant mathematical models. If the coefficients of stochastic differential equations are constant then the solutions in the explicit form are derived. On practice the derivatives of the interest rate processes are non-observed therefore the practical forms of solutions can not include the values of derivatives. Therefore it is discussed a problem of exclusion of these values from solutions. It is shown that these solutions exist and they are determined on discrete set of time instants. The case when the first derivative of process of interest rate has independent increments is described in details. The offered approach is illustrated by the analysis of actual time series of the yield rates of the US Treasury Securities

On fitting the autoregressive investment models to real financial data

The successful investment policy is an integral part of successful activity of the insurance company. The return to the shareholders of the insurance company usually thought of as comprising the underwriting result and investment income. The investment income is very important even for an insurance company, which writes mainly a short tail business. For the successful activity the insurance company needs the appropriate investment policy as well as in good investment control