In this article, we propose a numerical algorithm for computing price of discrete single and double barrier option under the emph{Black-Scholes} model. In virtue of some general transformations, the partial differential equations of option pricing in different monitoring dates are converted into simple diffusion equations. The present method is fast compared to alterna...

The cointegrated model considered here is a nonstationary vector autoregressive process in which some linear functions are stationary and others are random walks. The first difference of the process (the "error-correction form") is stationary. Statistical inference, such as reduced rank regression estimation of the coefficients of the process and tests of hypotheses of dimensionality of the sta...

The main goal of the paper is to investigate whether real GDP follows a trend stationary or a different stationary process. Our hypothesis is that real output is characterized by a non-linear mean reverting process. It is flexible Fourier stationary unit root test proposed by Enders and Lee (2004, 2009) to assess the nonstationary properties of the real GDP per capita that has been applied for ...

We study non-equilibrium reaction-diffusion processes with open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be determined in an elementary way. We give the equation which includes an auxiliary parameter and determines possible boundary conditions for the model to be solved exactly...

We study the effect of transport processes (diffusion and free–streaming) on a collapsing spherically symmetric distribution of matter in a self–similar space– time. A very simple solution shows interesting features when it is matched with the Vaidya exterior solution. In the mixed case (diffusion and free– streaming), we find a barotropic equation of state in the stationary regime. In the diff...

The objective of this note is to explore the existence of an effective bandwidth for ATM (asynchronous transfer mode) traffic. We show that such an effective bandwidth exists for a class of stationary Gaussian sources. We also show that the effective bandwidth cannot be defined for general non-stationary sources by providing an elementary counter-example.

the problem of discrimination between two stationary ar(p) plus noise processes is consideredwhen the noise process are different in two models. the discrimination rule leads to a quadratic form withcumbersome matrices. an approximate and analytic form is given to distribution of the discriminant. thesimulation study has been used to show the performance of discrimination rule. the cumulants of...

The notion of a locally stationary process is introduced by Silverman in [ l j . This is a new kind of a random process generalizing the notion of a weakly station­ ary process. Let {x(t)}, teR1bsa random process, generally complex, with vanishing mean value and finite covariance function R(s, t) = E{x(s) x(r)} on Wj x Mu where x(t) is the complex conjugate to x(r). The author of [ l j says tha...

Stationarity of a data set guarantees spatially invariant statistical properties, such as mean, variance, dip or spectrum. Many image processing schemes assume stationary data and consequently do not apply to nonstationary data. However, these processes can be generalized to apply to local-stationary data sets, a type of nonstationary data. We split the local-stationary data into its stationary...