We derive error estimates for approximate (viscosity) solutions of Bellman equations associated to controlled jump-diffusion processes, which are fully nonlinear integro-partial differential equations. Two main results are obtained: (i) error bounds for a class of monotone approximation schemes, which includes finite difference schemes, and (ii) bounds on the error induced when the original Lév...

Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Different from randomness and fuzziness, uncertainty theory provides a new mathematical model for uncertain phenomena. A key concept to describe uncertain quantity is uncertain variable, and expected value operator provides an average value of uncert...

The purpose of this paper is concerned with the existence extremal mild solutions for Sobolev type Hilfer fractional evolution equations nonlocal conditions in an ordered Banach spaces E. By using monotone iterative technique coupled method lower and upper solutions, help theory propagation family as well measure noncompactness Sadovskii?s fixed point theorem, we obtain some results equations. ...

We prove the existence of solutions for the Monge minimization problem, addressed in a metric measure space (X, d,m) enjoying the Riemannian curvature-dimension condition RCD∗(K,N), with N < ∞. For the first marginal measure, we assume that μ0 ≪ m. As a corollary, we obtain that the Monge problem and its relaxed version, the Monge-Kantorovich problem, attain the same minimal value. Moreover we ...

This paper extends the Choquet integral, widely used in multi-attribute decision problems, to the non monotone case in the context of Group Decision Theory. Even if not so often, preference structures which violate the monotonicity axiom can be observed in real applications. Our aim is twofold. First, we propose the Choquet integral with non monotone non additive measure. Then, we apply the Cho...

In this thesis, I design a Maximum Coverage problem with KnaPsack constraint (MCKP) based model for extractive multi-document summarization. The model integrates three measures to detect important sentences including Coverage, rewards sentences in regards to their representative level of the whole document, Relevance, focuses to select sentences that related to the given query, and Compression,...

This paper contains the following results for ecohomies with infinite dimensional commodity spaces. (i) We establish a core-Walras equivalence theorem for economies with an atomless measure space of agents and with an ordered separable Banach commodity space whose positive cone has a non-empty norm interior. This result includes as a special case the Aumann (1964) and Schmeidler-Hildenbrand [Hi...

We suggest a biased-bootstrap method for monotonising general linear, kernel-type estimators, for example local linear estimators and Nadaraya-Watson estimators. Attributes of our approach include the fact that it produces smooth estimates, that is applicable to a particularly wide range of estimator types, and that it can be employed after the smoothing step has been implemented. Therefore , a...

This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-Jacobi and SUR (Successive Under-Relaxation) methods are constructed. The monotone methods solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear monotone difference schemes. Convergent rates of...

We construct monotone numerical schemes for a class of nonlinear PDE for elliptic and initial value problems for parabolic problems. The elliptic part is closely connected to a linear elliptic operator, which we discretize by monotone schemes, and solve the nonlinear problem by iteration. We assume that the elliptic differential operator is in the divergence form, with measurable coefficients s...