Related papers: Path-dependent Poisson random measures and stochas…
The reciprocal class of a Markov path measure is the set of all mixtures of its bridges. We give characterizations of the reciprocal class of a continuous-time Markov random walk on a graph. Our main result is in terms of some reciprocal…
Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…
We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that…
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian…
The framework of Stein's method for Poisson process approximation is presented from the point of view of Palm theory, which is used to construct Stein identities and define local dependence. A general result (Theorem…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
We consider additive functionals of systems of random measures whose initial configuration is given by a Poisson point process, and whose individual components evolve according to arbitrary Markovian or non-Markovian measure valued…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
We present a new Bayesian inference method for compartmental models that takes into account the intrinsic stochasticity of the process. We show how to formulate a SIR-type Markov jump process as the solution of a stochastic differential…
A reinforcement algorithm introduced by H.A. Simon \cite{Simon} produces a sequence of uniform random variables with memory as follows. At each step, with a fixed probability $p\in(0,1)$, $\hat U_{n+1}$ is sampled uniformly from $\hat U_1,…
The Poisson process is one of the simplest stochastic processes defined in continuous time, having interesting mathematical properties, leading, in many situations, to applications mathematically treatable. One of the limitations of the…
We study systems of simple point processes that admit stochastic intensities. We represent these point processes as thinnings of Poisson measures and are interested in a convergence result of such systems. This result states that, if the…
We consider Poissonian pair correlations (PPC) for uniformly distributed sequences of random numbers with a dependency structure. More specifically, we treat two classes of dependent random variables which have widely been studied in the…
Recently the so-called Prabhakar generalization of the fractional Poisson counting process attracted much interest for his flexibility to adapt real world situations. In this renewal process the waiting times between events are IID…
Stochastic resetting has been a subject of considerable interest within statistical physics, both as means of improving completion times of complex processes such as searches and as a paradigm for generating nonequilibrium stationary…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
We consider random walks on the support of a random purely atomic measure on $\mathbb{R}^d$ with random jump probability rates. The jump range can be unbounded. The purely atomic measure is reversible for the random walk and stationary for…