Related papers: Concentration of scalar ergodic diffusions and som…
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…
In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…
The diffusion approximation of stochastic gradient descent (SGD) in current literature is only valid on a finite time interval. In this paper, we establish the uniform-in-time diffusion approximation of SGD, by only assuming that the…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications,…
This work provides reliable a posteriori error estimates for Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems. The classes of systems we study are quite general with a focus on convection-dominated…
In this paper, we establish novel concentration inequalities for additive functionals of geometrically ergodic Markov chains similar to Rosenthal inequalities for sums of independent random variables. We pay special attention to the…
The data processing inequality is central to information theory and motivates the study of monotonic divergences. However, it is not clear operationally we need to consider all such divergences. We establish a simple method for Pinsker…
The Pearson family of ergodic diffusions with a quadratic diffusion coefficient and a linear force are characterized by explicit dynamics of their integer moments and by explicit relaxation spectral properties towards their steady state.…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have…
This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this…
Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…
Diffusion of molecules in cells plays an important role in providing a biological reaction on the surface by finding a target on the membrane surface. The water retardation (slow diffusion) near the target assists the searching molecules to…
We consider the problem of estimating the joint distribution of a continuous-time perpetuity and the underlying factors which govern the cash flow rate, in an ergodic Markov model. Two approaches are used to obtain the distribution. The…
We use an analogy with the statistical mechanics of gas to build the statistical mechanics of granular media. The case of an isotropic disordered packing of equal spheres submitted to an isotropic stress is considered. We use the assumption…
Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…