Related papers: Strong and weak mean value properties on trees
We consider random processes that are history-dependent, in the sense that the distribution of the next step of the process at any time depends upon the entire past history of the process. In general, therefore, the Markov property cannot…
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
The main goal of this work is to provide an insight into the problem of discrimination of positive operator valued measures with rank-one effects. It is our intention to study multiple shot discrimination of such measurements, that is the…
We start to investigate how small changes on the definition of ordinary means affect their properties. Especially the property of being a mean. In that direction we are looking for weakenings of the basic defining property of means. Hence…
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…
We present an axiomatic approach to the mean and discuss generalizations of the mean, including one due to Kolmogorov based on the Weak Law of Large Numbers. We offer examples and counterexamples, describe conventional and unconventional…
We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds.…
We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges…
This note make the observation that property A for a space is equivalent to the existence of a Markov process on the space which has a (uniformly) trivial Poisson boundary.
We consider iterated function systems (finite or countable), together with linear and continuous operators on Hilbert spaces, which enable us to construct Markov-type operators. Under suitable conditions, these Markov-type operators have…
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…
Quantum work fluctuation theorems are known to hold when the work is defined as the difference between the outcomes of projective measurements carried out on the Hamiltonian of the system at the initial and the final time instants of the…
We first study labeled transition systems with explicit successful termination. We establish the notions of strong, weak, and branching bisimulation in terms of boolean matrix theory, introducing thus a novel and powerful algebraic…
In this paper, we prove the existence of a common end point for a pair of multivalued mappings satisfying a new generalized weakly contractive condition in a complete metric space. Our result generalizes and extends many known results.
A quantum transition can be seen as a result of interference between various pathways(e.g. Feynman paths) which can be labelled by a variable $f$. An attempt to determine the value of f without destroying the coherence between the pathways…
The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the…
This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated…
We examine weak measurements of arbitrary observables where the object is prepared in a mixed state and on which measurements with imperfect detectors are made. The weak value of an observable can be expressed as a conditional expectation…