Stochastic differential equations in R with random coefficients are considered where one continuous driving process admits a generalized quadratic variation process. The latter and the other driving processes are assumed to possess sample paths in the fractional Sobolev space W β 2 for some β > 1/2. The stochastic integrals are determined as anticipating forward integrals. A pathwise solution p...

This paper deals with the time-domain numerical calculation of electromagnetic (EM) fields in linearly dispersive media described by multipole Debye model. The frequency-dependent finite-difference time-domain (FD2TD) method is applied to solve Debye equations using convolution integrals or by direct integration. Original formulations of FD2TD methods are proposed using different approaches. In...

A stochastic calculus similar to Malliavin’s calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integral representation of square integrable Wiener f...

A boundary element formulation is presented in this work for transient heat conduction analysis of threedimensional (3D) fiber-reinforced materials. The cylindrical-shaped fibers in a 3D matrix are idealized by a system of curvilinear line elements with a prescribed diameter. The variations in the temperature and flux fields in the circumferential direction are represented in terms of a trigono...