In this paper we discuss stochastic di erential delay equations with Markovian switching. Such an equation can be regarded 9 as the result of several stochastic di erential delay equations switching from one to another according to the movement of a Markov chain. The aim of this paper is to investigate the stability in distribution of the equations. 11 c © 2003 Published by Elsevier Science B.V.

The di erential equation dX dt X k X where k is a Toeplitz annihilator has been suggested as a means to solve the inverse Toeplitz eigenvalue problem Starting with the diagonal matrix whose entries are the same as the given eigenvalues the solution ow has been observed numerically to always converge a symmetric Toeplitz matrix as t This paper is an attempt to understand the dynamics involved in...

The e¢ cient and accurate calculation of sensitivities of the price of …nancial derivatives with respect to perturbations of the parameters in the underlying model, the so called ‘Greeks’, remains a great practical challenge in the derivative industry. This is true regardless of whether methods for partial di¤erential equations or stochastic di¤erential equations (Monte Carlo techniques) are be...

The stability of the ow of an incompressible, viscous uid through a pipe of circular cross-section, curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is ob...

We develop the non-di erentiable embedding theory of di erential operators and Lagrangian systems using a new operator on non-di erentiable functions. We then construct the corresponding calculus of variations and we derive the associated non-di erentiable Euler-Lagrange equation, and apply this formalism to the study of PDE's. First, we extend the characteristics method to the non-di erentiabl...

The nite di erence method is a numerical analysis technique used to solve problems involving irregular geometries, complicated boundary conditions, or both. The geometries are represented using partial di erential equations. The solutions to the partial di erential equations can be easily generated with the aid of a computer. As the geometries become increasingly complex, the solutions of the p...

in this article, a mathematical model describing the growth orterminating myelogenous leukemia blood cancer's cells against naive t-celland eective t-cell population of body, presented by fractional dierentialequations. we use this model to analyze the stability of the dynamics, whichoccur in the local interaction of eector-immune cell and tumor cells. wewill also investigate the optima...

We investigate numerical valuation of cross-currency interest rate-based derivatives under Babbs' extended Vasicek-style model by numerical solution of the associated partial di erential equation (PDE) | in particular, we consider the terminable di erential (di ) swap. Firstly we precisely formulate, in terms of their cash ows, various types of single and cross-currency swaps and swaptions. We ...

The method of modi®ed equations is studied as a technique for the analysis of ®nite di€erence equations. The non-uniqueness of the modi®ed equation of a di€erence method is stressed and three kinds of modi®ed equations are introduced. The ®rst modi®ed or equivalent equation is the natural pseudo-di€erential operator associated to the original numerical method. Linear and nonlinear combinations ...

A large number of di erential equation problems which admit traveling waves have very large (typically in nite) naturally de ned domains, with boundary conditions de ned at the domain boundary. To be able to numerically solve these problems in smaller subdomains of the original domain, arti cial boundary conditions must be de ned for these subdomains. One such arti cal boundaryconditionswhich c...