Stochastic di erential games are considered in a non-Markovian setting. Typically, in stochastic di erential games the modulating process of the di usion equation describing the state ow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method i...

We introduce a robot-safety device system attended by two di erent repairmen. The twin system is characterized by the natural feature of cold standby and by an admissible “risky” state. In order to analyse the random behaviour of the entire system (robot, safety device, repair facility), we employ a stochastic process endowed with probability measures satisfying general steady-state di erential...

This paper describes the design philosophy behind the recent replacement of the NAG Ordinary Di erential Equation (ODE) sti integrators. This replacement was is intended to update the ODE chapter algorithmically but, more importantly in the context of this paper, it provides a more exible interface than has been available in the past. This interface is designed to permit a wide variety of probl...

After a series of application papers have proven the approach to be numerically e ective, this paper gives the rst theoretical foundation for methods solving partial di erential equations by collocation with (possibly radial) basis functions.

We present waveform relaxation of linear integral-di erential equations which occur in circuit simulation. We give su cient conditions for convergence and numerical experiments to verify the theoretical results.

We prove an existence and uniqueness theorem for backward stochastic di erential equations driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one.

An exact solution of a system of coupled di erential equations describing the dynamics of a special class of winner-take-all networks is given. From the solution two properties of the short-termmemory traces are derived: (1) information preservation and (2) a discrimination measure. These properties justify a biologically inspired fault tolerant extension of the network using di erentiating neu...

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...

Transfer functions models of linear systems are a well established tool for the design and analysis of one-dimensional systems. This is not the case for multidimensional physical systems, given in terms of initial boundary value problems. Here, the only mathematical description of widespread use are partial di erential equations. This contribution shows, how the one-dimensional transfer functio...

A new mixed formulation recently proposed for linear problems is extended to quasilinear second order elliptic problems This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated i e the scalar unknown its gradient and its ux the coe cients times the gradient Based on this formulation mixed nite element approximations of the quasilinear ...