Related papers: Regularity conditions in the realisability problem…
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…
This paper contains an answer to the question of existence of regularities of the so called \textit{random in a broad sense} mass phenomena, asked by A. N. Kolmogorov in \cite{Kolmogorov}. It turns out that some family of finitely-additive…
We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing data framework, we give a novel characterisation of the observed data as a stopping-set sigma algebra. We demonstrate that…
A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…
We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…
The aim of this paper is to give a simpler, more usable sufficient condition to the regularity of generic weakly stationary time series. Also, this condition is used to show how regular processes satisfying these sufficient conditions can…
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
Regular model checking is a well-established technique for the verification of regular transition systems (RTS): transition systems whose initial configurations and transition relation can be effectively encoded as regular languages. In…
The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
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…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
We investigate continuum percolation for Cox point processes, that is, Poisson point processes driven by random intensity measures. First, we derive sufficient conditions for the existence of non-trivial sub- and super-critical percolation…
We give necessary and sufficient conditions for a pair of (generalized) functions $\rho_1(\mathbf{r}_1)$ and $\rho_2(\mathbf{r}_1,\mathbf{r}_2)$, $\mathbf{r}_i\in X$, to be the density and pair correlations of some point process in a…
Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the…