Related papers: Image transformations, Markov operators, and sampl…

Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although…

Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…

We study the images of the Markov measures under transformations generated by the Mealy automata. We find conditions under which the image measure is absolutely continuous or singular relative to the Markov measure. Also, we determine…

We introduce a reversible Markovian coagulation-fragmentation process on the set of partitions of $\{1,\ldots,L\}$ into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be…

We study Markov multi-maps of the interval from the point of view of topological dynamics. Specifically, we investigate whether they have various properties, including topological transitivity, topological mixing, dense periodic points, and…

Markov combination is an operation that takes two statistical models and produces a third whose marginal distributions include those of the original models. Building upon and extending existing work in the Gaussian case, we develop Markov…

There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…

The geometric construction of the functional integral over coset spaces ${\cal M}/{\cal G}$ is reviewed. The inner product on the cotangent space of infinitesimal deformations of $\cal M$ defines an invariant distance and volume form, or…

This paper introduces an intrinsic theory of Thermodynamic Formalism for Iterated Functions Systems with general positive continuous weights (IFSw).We study the spectral properties of the Transfer and Markov operators and one of our first…

The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for zero-dimensional spaces in terms of regular extension operators having compact…

In this short note, we study the properties of the weighted Frechet mean as a convex combination operator on an arbitrary metric space, (Y,d). We show that this binary operator is commutative, non-associative, idempotent, invariant to…

We construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary…

It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact setting, for a large family of transitive countable Markov…

Image registration is a fundamental step in medical image analysis. Ideally, the transformation that registers one image to another should be a diffeomorphism that is both invertible and smooth. Traditional methods like geodesic shooting…

We consider the invariant measure of a homogeneous continuous- time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be…

Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can…

We associate to each iterated function system consisting of phi-max-contractions an operator (on the space of continuous functions from the shift space on the metric space corresponding to the system) having a unique fixed point whose image…

Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two…

The paper describes two Borel-measurable functions from a measure space into a locally convex space such that the image measure for each function is Radon but their sum is not Borel-measurable.

We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory…