Many applications from economic and financial practice lead to optimization problems depending on a probability measure. A complete knowledge of the "underlying" measure is a necessary assumption to determine an exact optimal solution and an exact optimal value. Since this condition is not...

A number of inverse problems may be viewed in terms of the approximation of a target element x in a complete metric space (X,d) by the fixed point x* of a contraction function T : X - X. In practice, from a family of contraction functions T(a) one wishes to find the parameter a for which the...

Economic and financial activities are often influenced simultaneously by a decision parameter and a random factor. Since mostly it is necessary to determine the decision parameter without knowledge of the realization of the random element, deterministic optimization problems depending on a...

Suppose that {Xt,t≥0} is a non-stationary Markov process, taking values in a Polish metric space E. We prove the law of large numbers and central limit theorem for an additive functional of the form ∫0Tψ(Xs)ds, provided that the dual transition probability semigroup, defined on measures, is...

In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least...

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal process- ing, mechanical ingeneering, psychometrics, and other fields under different names. It still bears the same mathematical idea: the...

In order to develop statistical tests for the Lyapunov exponents of deterministic dynamical systems, we develop bootstrap tests based on empirical likelihood for percentiles and expectiles of strictly stationary processes. The percentiles and expectiles are estimated in terms of asymmetric least...