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We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…
The analysis of high-dimensional dynamical systems generally requires the integration of simulation data with experimental measurements. Experimental data often has substantial amounts of measurement noise that compromises the ability to…
This paper is devoted to the well-posedness analysis of a nonstationary Stokes hemivariational inequality for an incompressible fluid flow described by the Stokes equations subject to a nonsmooth boundary condition of friction type…
We consider a general class of stochastic optimal control problems, where the state process lives in a real separable Hilbert space and is driven by a cylindrical Brownian motion and a Poisson random measure; no special structure is imposed…
Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant $\mathbb{R}_+$ of the $d$-dimensional Euclidean space and controlled by the reflections…
In this work, we consider a sensor selection drawn at random by a sampling with replacement policy for a linear time-invariant dynamical system subject to process and measurement noise. We employ the Kalman filter to estimate the state of…
We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…
Earth and soils are indispensable elements of river environment. Dam-downstream environment and ecosystems have been severely affected by reduced or even stopped sediment supply from the upstream. Replenishing earth and soils from outside…
This paper aims to make a new contribution to the study of lifetime ruin problem by considering investment in two hedge funds with high-watermark fees and drift uncertainty. Due to multi-dimensional performance fees that are charged…
Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…
We consider stochastic dynamic programming problems with high-dimensional, discrete state-spaces and finite, discrete-time horizons that prohibit direct computation of the value function from a given Bellman equation for all states and time…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
We consider a parameter estimation problem for one dimensional stochastic heat equations, when data is sampled discretely in time or spatial component. We prove that, the real valued parameter next to the Laplacian (the drift), and the…
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…
This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for…
In this paper we study the optimal stochastic control problem for stochastic differential systems reflected in a domain. The cost functional is a recursive one, which is defined via generalized backward stochastic differential equations…
We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal…
We consider a class of economic growth models that includes the classical Ramsey--Cass--Koopmans capital accumulation model and verify that, under several assumptions, the value function of the model is the unique viscosity solution to the…
We investigate propagation of convexity and convex ordering on a typical discrete-time stochastic optimal control problem, namely the pricing of swing option. The dynamics of the underlying asset is modelled by the Euler scheme of a…
We study a nonsmooth nonconvex optimization problem defined over nonconvex constraints, where the feasible set is given by the intersection of the closure of an open set and a smooth manifold. By endowing the open set with a Riemannian…