Abstract. When a randomly perturbed dynamical system is subject to some constraints, the trajectories of the system and the noise-induced most probable transition pathways are restricted on the manifold associated with the given constraints. We present a constrained minimum action method to compute the optimal transition pathways on manifolds. By formulating the constrained stochastic dynamics ...

In this paper we study the regularity of the solution of an elliptic partial di erential equation with discontinuous coe cients. This result is used to establish the continuous Fr echet di erentiability of a shape functional arising in the optimal shape design of an electromagnet.

"Monte Carlo simulation" in the context of option pricing refers to a set of techniques to generate underlying values–typically stock prices or interest rates–over time. Typically the dynamics of these stock prices and interest rates are assumed to be driven by a continuous-time stochastic process. Simulation, however, is done at discrete time steps. Hence, the …rst step in any simulation schem...

We de…ne the transient spectrum as the time-frequency spectrum of a random system undergoing a transient behavior. We show that the transient spectrum approaches the classical frequency spectrum when time goes to in…nity. We prove that it is always possible to decompose the transient spectrum into the sum of a stationary spectrum and a decaying spectrum. The stationary spectrum is, up to a cons...

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 ...

in this work, we conduct a comparative study among the combine laplace transform and modied adomian decomposition method (lmadm) and two traditional methods for an analytic and approximate treatment of special type of nonlinear volterra integro-differential equations of the second kind. the nonlinear part of integro-differential is approximated by adomian polynomials, and the equation is red...

Since the advent of Taylor Series, polynomial methods have been used to solve di↵erential equations and learn the properties of di↵erential equations. There are many polynomial methods for solving di↵erential equations and understanding dynamical systems. For example, Taylor polynomials, Chebyshev Polynomials and Adomian Polynomials are used to generate approximate solutions. Automatic di↵erent...

We consider global attractors Af of dissipative parabolic equations ut = uxx + f(x; u; ux) on the unit interval 0 x 1 with Neumann boundary conditions. A permutation f is de ned by the two orderings of the set of (hyperbolic) equilibrium solutions ut 0 according to their respective values at the two boundary points x = 0 and x = 1: We prove that two global attractors, Af and Ag, are globally C0...

This work introduces a generalised hybridisation strategy which utilises the information sharing mechanism deployed in Stochastic Di usion Search when applied to a number of population-based algorithms, e ectively merging this nature-inspired algorithm with some population-based algorithms. The results reported herein demonstrate that the hybrid algorithm, exploiting information-sharing within ...

Do long-term and short-term options contain di!erential information? If so, can long-term options better di!erentiate among alternative models? To answer these questions, we "rst demonstrate analytically that di!erences among alternative models usually may not surface when applied to short-term options, but do so when applied to longterm contracts. Using S&P 500 options and LEAPS, we "nd that s...