This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic di↵erential equations with random coe cients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a di↵erent line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by using b...

| We consider di erential equations A(x) _ x = g(x), where A is an n n-matrix of C 1 functions and g is C 1 . We investigate the above di erential equation about singular points x 0 that are standard in the sense of Rabier. In particular, the null space of A(x 0 ) is of dimension 1. We show that there is a C 1 -di eomorphism that transforms the above equation about x 0 into x 1 _ x 1 = 1, _ x 2...

We describe an object oriented MATLAB toolbox for solving di erential equations on manifolds. The software re ects recent development within the area of geometric integration. Through the use of elements from di erential geometry, in particular Lie groups and homogeneous spaces, coordinate free formulations of numerical integrators are developed. The strict mathematical de nitions and results a...

A system of a parabolic partial di erential equation coupled with ordinary di erential inclusions that arises from a closed-loop control problem for a thermodynamic process governed by the Allen-Cahn di usion reaction model is studied. A feedback law for the closed-loop control is proposed and implemented in the case of a nite number of control devices located inside the process domain basing o...

We present four circuits implemented in subthreshold CMOS which greatly increase the linear range over the basic di erential pair. These circuits are appropriate for low voltage applications since there is no stacking of saturated transistors. The rst circuit topology employs multiple asymmetric di erential pairs. The second is a symmetric \bump" transconductor. The remaining two use source deg...

A lot of works has been devoted to stability analysis of a stationary point for linear and non-linear systems of stochastic di erential equations. Here we consider the stability of an invariant compact manifold of a non-linear system. To this end we derive a linearized system for orthogonal displacements of a solution from the manifold. We introduce notions of Lyapunov exponents, moment Lyapuno...

In earlier work we constructed a class of spherically symmetric, ̄uid dynamical shock waves that satisfy the Einstein equations of general relativity. These shock waves extend the celebrated Oppenheimer-Snyder result to the case of non-zero pressure. Our shock waves are determined by a system of ordinary di€erential equations that describe the matching of a FriedmannRobertson-Walker metric (a c...

A new algorithm of determination of coe cients of multidimensional heat equations on the basis of temperature measurements is proposed. A system of stochastic di erential equations (SDE) can be assigned to a linear multidimensional heat equation. The solution of the heat equation can be obtained by solving the corresponding SDE by the method of statistical modeling. The sensitivity analysis is ...

The present paper gives a new view point for the di erential operators with respect to the coordinates of the quantum matrix space. A special emphasis is put on an inductive construction of these di erential operators from the q-di erence operators de ned on each columns (resp. rows). This idea for understanding our operators provides us with two important applications: (1) a construction of th...

The stability in L norm is considered for the Ritz Volterra projection and some applications are presented in this paper As a result point wise error estimates are established for the nite ele ment approximation for the parabolic integro di erential equation Sobolev equations and a di usion equation with non local boundary value problem This work is supported in part by NSERC CANADA Journal of ...