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We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…

This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a…

Taking the Fourier integral theorem as our starting point, in this paper we focus on natural Monte Carlo and fully nonparametric estimators of multivariate distributions and conditional distribution functions. We do this without the need…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

We introduce a hull operator on Poisson point processes, the easiest example being the convex hull of the support of a point process in Euclidean space. Assuming that the intensity measure of the process is known on the set generated by the…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

Point process modeling is gaining increasing attention, as point process type data are emerging in numerous scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression…

We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…

Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…

We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…

In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…

This survey is a preliminary version of a chapter of the forthcoming book "Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-It\^o Chaos Expansions and Stochastic Geometry" edited by Giovanni Peccati and Matthias…

In a Cox model, the partial likelihood, as the product of a series of conditional probabilities, is used to estimate the regression coefficients. In practice, those conditional probabilities are approximated by risk score ratios based on a…

We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…

A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view…

In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is…

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

In this paper, we consider a stochastic model based on the Cox- Ingersoll- Ross model (CIR). The stochastic model is parameterized analytically by applying It\^o's calculus and the trend functions of the proposed process is calculated. The…

This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and…

We develop a framework for stochastic portfolio theory (SPT), which incorporates modern nonlinear price impact and impact decay models. Our main result is the derivation of the celebrated master formula for additive functional generation of…