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...

Four types of global error for initial value problems are considered in a common framework. They include classical forward error analysis and shadowing error analysis together with extensions of both to rescaling of time. To determine the amplification of the local error that bounds the global error we present a linear analysis similar in spirit to condition number estimation for linear systems...

Oberwolfach Tagungsbericht 26/1999 Partial Di erential Equations 13.06.1999 { 19.06.1999 This meeting was organized by L. C. Evans (Berkeley), S. M uller (MPI Leipzig) and E. Kuwert (Freiburg). The 22 delivered talks addressed a broad spectrum of questions for nonlinear partial di erential equations. Most of the considered problems arise in geometry or in physics, as for example submanifolds w...

Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...

We consider a system of ordinary di erential equations consisting of a singularly perturbed scalar di erential equation of second order and a scalar di erential equation of rst or second order and study a Neuman-Cauchy or a Neuman-Dirichlet problem. We assume that the degenerate equation has two intersecting solutions such that the standard theory for systems of Tichonov's type cannot be applie...

In this paper we give necessary design principles to be used, when constructing secure Feistel ciphers. We introduce a new concept, practical security against linear and di erential attacks on Feistel ciphers. We give examples of such Feistel ciphers (practically) resistant to di erential attacks, linear attacks and other attacks.

This course provides an introduction to the interplay between linear algebra and di¤erential equations/dynamical systems in continuous time. We …rst introduce linear di¤erential equations in Euclidian space R and on Grassmannian and ‡ag manifolds induced by a single matrix A, with emphasis on characterizations of the constant matrix A from a dynamics point of view. We then introduce linear skew...

This paper surveys recent results on the classi cation of di erential invari ants of transformation groups and their applications to invariant di erential equations and variational problems Consider a group of transformations acting on a jet space coordinatized by the inde pendent variables the dependent variables and their derivatives Scalar functions which are not a ected by the group transfo...

Matrix Di erential Riccati Equations (MDREs) X = A21 XA11 + A22X XA12X; X(0) = X0; where Aij Aij(t), appear frequently throughout applied mathematics, science, and engineering. MDREs play particularly important roles in optimal control, ltering, estimation, and in two-point linear boundary value problems. In the past a number of unconventional numerical methods that are suited only for time-inv...