Related papers: Loop-free Markov chains as determinantal point pro…

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition densities are proved. The observation time [0,T] may be fixed or lim n T = 0, where nh = T and h is a mesh…

We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property…

Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…

Consider the random set composed of particles initially distributed on Zd, d >= 2, according to a Poisson point process of intensity u > 0 and moving as independent simple symmetric random walks, the trap particles. We are interested in the…

We analyze the statistical properties of a temporal point process driven by a confined fractional Brownian motion. The event count distribution and power spectral density of this non--Markovian point process exhibit power--law scaling. We…

We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables…

The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law of…

We prove a functional limit theorem for Markov chains that, in each step, move up or down by a possibly state dependent constant with probability $1/2$, respectively. The theorem entails that the law of every one-dimensional regular…

When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…

When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This can be done by considering as basic uncertainty models the so-called credal sets that…

We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…

Although introduced in the case of Poisson random measures, the lent particle method applies as well in other situations. We study here the case of marked point processes. In this case the Malliavin calculus (here in the sense of Dirichlet…

In this paper, we give an overview of mean drift conditions for the state-space classification of discrete-time Markov Chains and we present a new transience criterion for uniformly bounded Markov Chains with asymptotically zero drift. The…

Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…

We consider a sequence of matrices that are associated to Markov dynamical systems and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix…

The theory of quantum jump trajectories provides a new framework for understanding dynamical phase transitions in open systems. A candidate for such transitions is the atom maser, which for certain parameters exhibits strong intermittency…

We prove several results concerning classifications, based on successive observations $(X_1,..., X_n)$ of an unknown stationary and ergodic process, for membership in a given class of processes, such as the class of all finite order Markov…

The normalised partial sums of values of a nonnegative multiplicative function over divisors with appropriately restricted sizes of a random permutation from the symmetric group define trajectories of a stochastic process. We prove a…

We consider a sequence of Markov chains $(\mathcal X^n)_{n=1,2,...}$ with $\mathcal X^n = (X^n_\sigma)_{\sigma\in\mathcal T}$, indexed by the full binary tree $\mathcal T = \mathcal T_0 \cup \mathcal T_1 \cup ...$, where $\mathcal T_k$ is…

The branching rule is one of the most fundamental properties of the Macdonald symmetric polynomials. It expresses a Macdonald polynomial as a nonnegative linear combination of Macdonald polynomials with smaller number of variables. Taking a…