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In this note we connect the notion of solutions of a martingale problem to the notion of a strongly continuous and locally equi-continuous semigroup on the space of bounded continuous functions equipped with the strict topology. This…
We study a system of equations arising in the Chern-Simons model on finite graphs. Using the iteration scheme and the upper and lower solutions method, we get existence of solutions in the non-critical case. The critical case is dealt with…
The aim of this paper is to investigate extremum problems with pay-off being the total variational distance metric defined on the space of probability measures, subject to linear functional constraints on the space of probability measures,…
The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…
In this paper, we give sharp Rusak- and Markov-type inequalities for rational functions on several intervals when the system of intervals is a \textquotedblleft rational function inverse image\textquotedblright\, of an interval and those…
We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with the process. Applications to semi-Dirichlet forms are…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
The complexity of Pareto fronts imposes a great challenge on the convergence analysis of multi-objective optimization methods. While most theoretical convergence studies have addressed finite-set and/or discrete problems, others have…
We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrange\-ment-invariant class…
This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite…
This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area of extreme events, underlining its…
Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
Paper is devoted to extremal problems in geometric function theory of complex variables associated with estimates of functionals defined on the systems of non-overlapping domains. In particular, we strengthen some known result in this…
In this paper we obtain a generalization of some integral inequalities related to Chebyshev`s functional by using a generalized Katugampola fractional integral.
We expose in full detail a constructive procedure to invert the so--called "finite Markov moment problem". The proofs rely on the general theory of Toeplitz matrices together with the classical Newton's relations.
We utilize operational methods to generalize the Chernoff inequality and prove a new result that relates the moment bound to strictly absolute monotonic functions. We show that the Chernoff bound is part of a continuum of probability…
In this paper we survey the almost sure central limit theorem and its functional form (quenched) for stationary and ergodic processes. For additive functionals of a stationary and ergodic Markov chain these theorems are known under the…