Related papers: On forward-backward SDE approaches to continuous-t…
We consider two nonlinear state estimation problems in a setting where an extended Kalman filter receives measurements from two sets of sensors via two channels (2C). In the stochastic-2C problem, the channels drop measurements…
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution…
This paper introduces a spatio-temporal resonator model and an inference method for detection and estimation of nearly periodic temporal phenomena in spatio-temporal data. The model is derived as a spatial extension of a stochastic harmonic…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
This paper describes an optimization framework to design guidance for a possibly heterogeneous team of multiple mobile sensors to estimate a spatiotemporal process modeled by a 2D diffusion-advection process. Owing to the abstract linear…
This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. We…
In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any…
In areas such as finance, engineering, and science, we often face situations that change quickly and unpredictably. These situations are tough to handle and require special tools and methods capable of understanding and predicting what…
This paper investigates the $H_{2}/H_{\infty}$ control problem for linear stochastic differential systems under partial observation. Unlike existing studies that assume full state accessibility, we consider the scenario where the controller…
This paper addresses the numerical solution of backward stochastic differential equations (BSDEs) arising in stochastic optimal control. Specifically, we investigate two BSDEs: one derived from the Hamilton-Jacobi-Bellman equation and the…
In inverse problems, the goal is to estimate unknown model parameters from noisy observational data. Traditionally, inverse problems are solved under the assumption of a fixed forward operator describing the observation model. In this…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
In this paper, we present an optimal filter for linear time-varying continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. We first show that the unknown inputs…
Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are…
A backward stochastic differential equation (BSDE) is an SDE of the form $-dY_t = f(t,Y_t,Z_t)dt - Z_t^*dW_t;\ Y_T = \xi$. The subject of BSDEs has seen extensive attention since their introduction in the linear case by Bismut (1973) and in…
A novel approximate Bayesian filter based on backward stochastic differential equations is introduced. It uses a nonlinear Feynman--Kac representation of the filtering problem and the approximation of an unnormalized filtering density using…
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
This paper proposes a parallel-in-time method for computing continuous-time maximum-a-posteriori (MAP) trajectory estimates of the states of partially observed stochastic differential equations (SDEs), with the goal of improving…
This article is concerned with the convergence of the state estimate obtained from the discrete time Kalman filter to the continuous time estimate as the temporal discretization is refined. We derive convergence rate estimates for different…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…