相关论文: Robust $H_\infty$ Filtering for Nonlinear Discrete…

This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process $\nu$ whose components have paths of bounded variation. The presence of the process $\nu$ prevents from…

We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a bounded domain with oblique boundary conditions. These equations appear naturally in…

Stochastic volatility models have existed in Option pricing theory ever since the crash of 1987 which violated the Black-Scholes model assumption of constant volatility. Heston model is one such stochastic volatility model that is widely…

Effects of non-stationarity on the performance of hybrid ensemble filters are studied (by hybrid filters we mean those which blend ensemble covariances with some other regularizing covariances). To isolate effects of non-stationarity from…

A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…

Hamilton-Jacobi (HJ) reachability provides formal safety guarantees for nonlinear systems. However, it becomes computationally intractable in high-dimensional settings, motivating learning-based approximations that may introduce unsafe…

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…

In this paper, we prove several new results that give new insights into bilinear systems. We discuss conditions for asymptotic stability using probabilistic arguments. Moreover, we provide a global characterization of reachability in…

We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…

Robust control seeks stabilizing policies that perform reliably under adversarial disturbances, with $\mathcal{H}_\infty$ control as a classical formulation. It is known that policy optimization of robust $\mathcal{H}_\infty$ control…

We present ProbReach, a tool for verifying probabilistic reachability for stochastic hybrid systems, i.e., computing the probability that the system reaches an unsafe region of the state space. In particular, ProbReach will compute an…

The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propagate uncertainty through the state transitions and output…

This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…

The stochastic block model (SBM) is a flexible probabilistic tool that can be used to model interactions between clusters of nodes in a network. However, it does not account for interactions of time varying intensity between clusters. The…

A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial…

This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…

This paper is concerned with the development and use of duality theory for a hidden Markov model (HMM) with white noise observations. The main contribution of this work is to introduce a backward stochastic differential equation (BSDE) as a…

A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak…

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…

Sampling from probability densities is a common challenge in fields such as Uncertainty Quantification (UQ) and Generative Modelling (GM). In GM in particular, the use of reverse-time diffusion processes depending on the log-densities of…