Discrete inequalities, in particular the discrete analogues of the Gronwall–Bellman inequality, have been extensively used in the analysis of finite difference equations. The aim of the present paper is to establish some fractional difference inequalities of Gronwall–Bellman type which provide explicit bounds for the solutions of fractional difference equations.

We obtain error bounds for monotone approximation schemes of Hamilton-Jacobi-Bellman equations. These bounds improve previous results of Krylov and the authors. The key step in the proof of these new estimates is the introduction of a switching system which allows the construction of approximate, (almost) smooth supersolutions for the Hamilton-Jacobi-Bellman equation.

We derive error estimates for certain approximate solutions of Bellman equations associated to a class of controlled jump-diffusion (Lévy) processes. These Bellman equations are fully nonlinear degenerate integroPDEs interpreted in the sense of viscosity solutions. The approximate solutions are generated by an implicit finite difference-quadrature scheme.

Large industrial-scale databases tend to be poorly structured, dirty, and very confusing. There are many reasons for this disorder, not the least of which is that the application domains themselves are poorly structured, dirty and confusing. As data analysts, we are often called upon to mine, clean, or otherwise analyze these databases. In this article, we describe the types of problems we have...