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We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
We consider statistical inference in factor analysis for ergodic and non-ergodic diffusion processes from discrete observations. Factor model based on high frequency time series data has been mainly discussed in the field of high…
Given data generated by an observable stochastic process, we study how to construct statistically optimal decisions for general stochastic optimization problems. Our setting encompasses non-standard data structures, including data…
Multidimensional hypoelliptic diffusions arise naturally in different fields, for example to model neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. In this paper we…
We consider the setting of multiscale overdamped Langevin stochastic differential equations, and study the problem of learning the drift function of the homogenized dynamics from continuous-time observations of the multiscale system. We…
The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assumptions on the divergence free drift term, enabling us to…
We show that unconverged stochastic gradient descent can be interpreted as a procedure that samples from a nonparametric variational approximate posterior distribution. This distribution is implicitly defined as the transformation of an…
We consider a Poisson equation in $\mathbb R^d$ for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients.…
This paper considers the distributed computation of confidence regions tethered to multidimensional parameter estimation under linear measurement models. In particular, the considered confidence regions are non-asymptotic, this meaning that…
The advances in conic optimization have led to its increased utilization for modeling data uncertainty. In particular, conic mean-risk optimization gained prominence in probabilistic and robust optimization. Whereas the corresponding conic…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
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 present discrete-time approximation of optimal control policies for infinite horizon discounted/ergodic control problems for controlled diffusions in $\Rd$\,. In particular, our objective is to show near optimality of optimal policies…
We propose a nonparametric estimation for a class of fractional stochastic differential equations (FSDE) with random effects. We precisely consider general linear fractional stochastic differential equations with drift depending on random…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
In many applications, it is often necessary to sample the mean value of certain quantity with respect to a probability measure {\mu} on the level set of a smooth function $\xi: \mathbb{R}^d\rightarrow \mathbb{R}^k$, $1\le k < d$. A…
We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The…
This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The resulting effective deterministic model is given through a quasilocal discrete integral…
We consider statistical inference for a class of dynamic mixed-effect models described by stochastic differential equations whose drift and diffusion coefficients simultaneously depend on fixed- and random-effect parameters. Assuming that…
We study an ergodic singular control problem with constraint of a regular one-dimensional linear diffusion. The constraint allows the agent to control the diffusion only at jump times of independent Poisson process. Under relatively weak…