Related papers: Statistical Inference in Fractional Poisson Ornste…
We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small L\'{e}vy noises. We do not impose any moment condition on the driving L\'{e}vy process. Under certain regularity conditions…
In this article we study the asymptotic behaviour of the realized quadratic variation of a process $\int_{0}^{t}u_{s}dY_{s}^{(1)}$% , where $u$ is a $\beta$-H\"older continuous process with $\beta > 1-H$ and…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
This paper deals with U-statistics of Poisson processes and multiple Wiener-It\^o integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration…
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…
We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a…
We consider an ensemble of Ornstein-Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable…
In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially…
We study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an Ornstein-Uhlenbeck noise. This system undergoes a noise-induced bifurcation when the amplitude of the noise…
We generate the fractional Poisson process by subordinating the standard Poisson process to the inverse stable subordinator. Our analysis is based on application of the Laplace transform with respect to both arguments of the evolving…
Using the path integral representation of the non-equilibrium dynamics, we compute the most probable path between arbitrary starting and final points, followed by an active particle driven by persistent noise. We focus our attention on the…
We consider the problem of parameter estimation in the case of observation of the trajectory of diffusion process. We suppose that the drift coefficient has a singularity of cusp-type and the unknown parameter corresponds to the position of…
Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…
Dynamical scaling is an asymptotic property typical for the dynamics of first-order phase transitions in physical systems and related to self-similarity. Based on the integral-representation for the marginal probabilities of a fractional…
Using a coupling for the weighted sum of independent random variables and the explicit expression of the transition semigroup of Ornstein-Uhlenbeck processes driven by compound Poisson processes, we establish the existence of a successful…
We show that planar Bargmann-Fock percolation is noise sensitive under the Ornstein-Ulhenbeck process. The proof is based on the randomized algorithm approach introduced by Schramm and Steif and gives quantitative polynomial bounds on the…
We study the long time behavior of an Ornstein-Uhlenbeck process under the influence of a periodic drift. We prove that, under the standard diffusive rescaling, the law of the particle position converges weakly to the law of a Brownian…
In this paper, we present a method for factor analysis of discrete data. This is accomplished by fitting a dependent Poisson model with a factor structure. To be able to analyze ordinal data, we also consider a truncated Poisson…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
We review the probabilistic properties of Ornstein-Uhlenbeck processes in Hilbert spaces driven by L\'{e}vy processes. The emphasis is on the different contexts in which these processes arise, such as stochastic partial differential…