Related papers: Stochastic analysis for the Dirichlet--Ferguson pr…

We consider some fractional extensions of the recursive differential equation governing the Poisson process, by introducing combinations of different fractional time-derivatives. We show that the so-called "Generalized Mittag-Leffler…

Pitman~(1999) describes a duality relationship between fragmentation and coagulation operators. An explicit relationship is described for the two-parameter Poisson-Dirichlet laws, with parameters {\footnotesize $(\alpha,\theta)$} and…

Pitman(2003)(and subsequently Gnedin and Pitman (2006) showed that a large class of random partitions of the integers derived from a stable subordinator of index $\alpha\in(0,1)$ have infinite Gibbs (product) structure as a characterizing…

We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some complex power of the Riemann zeta function. We obtain asymptotic expansions resembling those provided by the Selberg-Delange method in…

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes $N_\alpha(t)$, $N_\beta(t)$, $t>0$, we show that $N_\alpha(N_\beta(t))…

We study the long-time convergence of a Fleming-Viot process, in the case where the underlying process is a metastable diffusion killed when it reaches some level set. Through a coupling argument, we establish the long-time convergence of…

Time series data may exhibit clustering over time and, in a multiple time series context, the clustering behavior may differ across the series. This paper is motivated by the Bayesian non--parametric modeling of the dependence between the…

It is shown that the new formula for the field theory Poisson brackets arise naturally in the extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields,…

This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…

The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…

The Malliavin derivative, divergence operator, and the Ornstein-Uhlenbeck operator are extended from the traditional Gaussian setting to generalized processes from the higher-order chaos spaces.

This paper provides a general and abstract approach to approximate ergodic regimes of Markov and Feller processes. More precisely, we show that the recursive algorithm presented in Lamberton & Pages (2002) and based on simulation algorithms…

We consider stochastic gradient estimation using only black-box function evaluations, where the function argument lies within a probability simplex. This problem is motivated from gradient-descent optimization procedures in multiple…

This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…

Let $p_1 \ge p_2 \ge \dots$ be the prime factors of a random integer chosen uniformly from $1$ to $n$, and let $$ \frac{\log p_1}{\log n}, \frac{\log p_2}{\log n}, \dots $$ be the sequence of scaled log factors. Billingsley's Theorem…

Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an It\^{o}…

This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of M\'etivier and Pellaumail which is quite restrictive. We make use of the notion of…

We study fundamental properties of the gamma process and their relation to various topics such as Poisson-Dirichlet measures and stable processes. We prove the quasi-invariance of the gamma process with respect to a large group of linear…

The work presents a proof of convergence of the density of energy levels to a Gaussian distribution for a wide class of quadratic forms of Fermi operators. This general result applies also to quadratic operators with disorder, e.g.,…

We consider a general McKean-Vlasov stochastic differential equation driven by a rotationally invariant $\alpha$-stable process on $\mathbb{R}^d$ with $\alpha \in (1,2)$. We assume that the diffusion coefficient is the identity matrix and…