相关论文: Optimal response for stochastic differential equat…
Let $a\in\mathbb{R}$ denote an unknown stationary target with a known distribution $\mu\in\mathcal{P(\mathbb{R}})$, the space of probability measures on $\mathbb{R}$. A diffusive searcher $X(\cdot)$ sets out from the origin to locate the…
We consider the problem of estimating a function defined over $n$ locations on a $d$-dimensional grid (having all side lengths equal to $n^{1/d}$). When the function is constrained to have discrete total variation bounded by $C_n$, we…
The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is…
In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first…
We examine the sensitivity properties of backward stochastic differential equations and reflected backward stochastic differential equations, which naturally arise in the context of optimal control and optimal stopping problems. Motivated…
We discuss the effective diffusion constant $D_{{\it eff}}$ for stochastic processes with spatially-dependent noise. Starting from a stochastic process given by a Langevin equation, different drift-diffusion equations can be derived…
In this paper we develop linear transfer Perron Frobenius operator-based approach for optimal stabilization of stochastic nonlinear system. One of the main highlight of the proposed transfer operator based approach is that both the theory…
We investigate the discrete-time stochastic linear quadratic control problem for a population of cooperative agents under the hard equality constraint on total control inputs, motivated by demand response in renewable energy systems. We…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on $L_p$-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data…
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a…
We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic…
Increasing penetration of wind and renewable generation poses significant challenges to the power system operations and reliability. This paper considers the real-time optimal transmission switching (OTS) problem for determining the…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
Perturbed Einstein's equations with a linear response relation and a stochastic source, applicable to a relativistic star model are worked out . These perturbations which are stochastic in nature, are of significance for building a…
It is a longstanding unsolved problem to characterize the optimal feedback controls for general linear quadratic optimal control problem of stochastic evolution equation with random coefficients. A solution to this problem is given in [21]…
Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model…