In this paper we consider the problem of estimating the state, and identifying parameters of a diffusion process, when the only available information is the crossing times of a boundary. By using a partial differential equation approach related with the computation of boundary–crossing probabilities, we derive finite dimensional reconstructors (filters) for the state and Feynman Kac type functi...

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...

A lattice Boltzmann model for multispecies flows with catalytic reactions is developed, which valid from very low to high surface Damk\"ohler numbers (${\text{Da}}_{\text{s}}$). The previously proposed [S. Arcidiacono, J. Mantzaras, and I. V. Karlin, Phys. Rev. E 78, 046711 (2008)], applicable low-to-moderate ${\text{Da}}_{\text{s}}$ encompasses part of the mixed kinetics transport-controlled r...

The correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary world sheets, can be expressed in terms of Wilson graphs in appropriate three-manifolds. We present a systematic approach to boundary conditions that break bulk symmetries. It is based on the construction, by ‘α-induction’, of a fusion ring for the bo...