In this paper we study a finite volume approximation for the conservative formulation of multiple fragmentation models. We investigate the convergence of the numerical solutions towards a weak solution of the continuous problem by considering locally bounded kernels. The proof is based on the Dunford-Pettis theorem by using the weak L compactness method. The analysis of the method allows us to ...

Contents Chapter 1. Martingales, continued 1 1.1. Martingales indexed by partially ordered sets 1 1.2. Notions of convergence for martingales 3 1.3. Uniform integrability 4 1.4. Convergence of martingales with directed index sets 6 1.5. Application: The 0-1 law of Kolmogorov 8 1.6. Continuous-time martingales 9 1.7. Tail bounds for martingales 12 1.8. Application: The Pólya urn 13 1.9. Applicat...

Let ( t )t∈R+ be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure π . We investigate the rates of convergence of the transition function P t (x, ·) to π ; specifically, we find conditions under which r(t)‖P t (x, ·)−π‖ → 0 as t → ∞, for suitable subgeometric rate functions r(t), where ‖ · ‖ denotes the usual total variation norm for a ...

We propose an extension of Newton’s Method for unconstrained multiobjective optimization (multicriteria optimization). The method does not scalarize the original vector optimization problem, i.e. we do not make use of any of the classical techniques that transform a multiobjective problem into a family of standard optimization problems. Neither ordering information nor weighting factors for the...

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

A [semi-]continuous real function of a frame (locale) L has up to now been understood as a frame homomorphism from the frame L(R) of reals into L [as a frame homomorphism (modulo some conditions) from certain subframes of L(R) into L]. Thus, these continuities involve different domains. It would be desirable if all these continuities were to have L(R) as a common domain. This paper demonstrates...