In this paper we solve a long-standing open problem by showing that strict superposition|that is, superposition without equality factoring|is refutationally complete. The diiculty of the problem arises from the fact that the strict calculus, in contrast to the standard calculus with equality factoring, is not compatible with arbitrary removal of tautologies, so that the usual techniques for pro...

We consider optimal stopping problems with finite-time horizon and state-dependent discounting. The underlying process is a one-dimensional linear diffusion the gain function time-homogeneous difference of two convex functions. Under mild technical assumptions local nature we prove fine regularity properties boundary including its continuity strict monotonicity. latter was never proven probabil...

We consider the linear programming approach for constrained and unconstrained Markov decision processes (MDPs) under long-run average-cost criterion, where class of MDPs in our study have Borel state spaces discrete countable action spaces. Under a strict unboundedness condition on one-stage costs recently introduced majorization transition stochastic kernel, we infinite-dimensional programs pr...

In this paper we introduce a new class of quasilinear elliptic equations driven by the so-called double phase operator with variable exponents. We prove certain properties corresponding Musielak-Orlicz Sobolev spaces (an equivalent norm, uniform convexity, Radon-Riesz property respect to modular) and (continuity, strict monotonicity, (S+)-property). contrast known constant exponent case are abl...

An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is ...