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The development level assessment and categorization of Croatian local and regional units is based on the value of the development index which is the main instrument of Croatian regional policy. The development index is a composite indicator calculated as a weighted average of five socioeconomic indicators. The goal of this paper is to analyze the uncertainty and sensitivity of the development index that arise from the procedures and indicators used in its construction. This analysis is then used to propose useful guidelines for future impovements. The methodology of the Croatian regional development index has been critically reviewed, revealing problems of multicollinearity and the existence of outliers. An empirical and relatively more objective multivariate approach for weight selection has been proposed. The uncertainty and sensitivity analysis were conducted using Monte Carlo simulations and variance-based techniques. Instead of a unique point estimate for the development level of territorial units an alternative confidence interval approach was considered.

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We examine three equivalent constructions of a censored symmetric purely discontinuous Lévy process on an open set D; via the corresponding Dirichlet form, through the Feynman-Kac transform of the Lévy process killed outside of D and from the same killed process by the Ikeda-Nagasawa-Watanabe piecing together procedure. By applying the trace theorem on n-sets for Besov-type spaces of generalized smoothness associated with complete Bernstein functions satisfying certain scaling conditions, we analyze the boundary behaviour of the corresponding censored Lévy process and determine conditions under which the process approaches the boundary ∂D in finite time. Furthermore, we prove a stronger version of the 3G inequality and its generalized version for Green functions of purely discontinuous Lévy processes on κ-fat open sets. Using this result, we obtain the scale invariant Harnack inequality for the corresponding censored process.

Given a subset D of the Euclidean space, we study nonlocal quadratic forms that take into account tuples (x, y) ∈ D × D if and only if the line segment between x and y is contained in D. We discuss regularity of the corresponding Dirichlet form leading to the existence of a jump process with visibility constraint. Our main aim is to investigate corresponding Poincaré inequalities and their scaling properties. For dumbbell shaped domains we show that the forms satisfy a Poincaré inequality with diffusive scaling. This relates to the rate of convergence of eigenvalues in singularly perturbed domains.