A transformation is introduced to e!ectively remove level e!ects, i.e. the state dependency of the di!usion function, in a restricted class of multivariate stochastic di!erential equations such that the general continuous}discrete-time nonlinear "ltering problem may be solved using new or existing implementations of the extended kalman "lter (EKF). An implementation of a quasi-maximum likelihoo...

In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting di usion processes. The particle syste...

In general, a comparison Lemma for the solutions of Forward-Backward Stochastic Di erential Equations (FBSDE) does not hold. Here we prove one for the backward component at the initial time, relying on certain monotonicity conditions on the coeÆcients of both components. Such a result is useful in applications. Indeed, one can use FBSDE's to de ne a utility functional able to capture the disapp...

This paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an appr...

This work is our rst attempt in establishing the connections between evolutionary computation algorithms and stochastic approximation procedures By treating evo lutionary algorithms as recursive stochastic procedures we study both constant gain and decreasing step size algorithms We formulate the problem in a rather general form supply the su cient conditions for convergence both with probabili...

In this study we analyze a non-overlapping domain decomposition method for the solution of elliptic Partial Di erential Equation (PDE) problems. This domain decomposition method involves the solution of Dirichlet and Neumann PDE problems on each subdomain, coupled with smoothing operations on the interfaces of the subdomains. The convergence analysis of the method at the di erential equation le...

Let us consider the di erential equation

Let X be the solution of an Itô di erential equation with jumps over R. Under some auxiliary assumptions on the parameters of the equation, we characterize the support of the law of X in the Skorohod space D as the closure of the set of solutions to piecewise ordinary di erential equations. This gives an analogue in the Poisson space to the classical Stroock–Varadhan support theorem. c © 2000 P...

We here provide two sided bounds for the density of the solution of a system of n di erential equations of dimension d, the rst one being forced by a non-degenerate random noise and the n− 1 other ones being degenerate. The system formed by the n equations satis es a suitable Hörmander condition: the second equation feels the noise plugged into the rst equation, the third equation feels the noi...

In this paper, we study the existence and stability of traveling waves in lattice dynamical systems, in particular, in lattice ordinary di erential equations (lattice ODE's) and in coupled map lattices (CML's). Instead of employing the moving coordinate approach as for partial di erential equations, we construct a local coordinate system around a traveling wave solution of a lattice ODE, analog...