相关论文: Uncertain dynamical systems defined by pseudomeasu…

Despite substantial improvement in the development of forecasting approaches, conditional and dynamic uncertainty estimates ought to be accommodated in decision-making in power system operation and market, in order to yield either…

One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with…

Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…

This paper provides a semiparametric model of estimating states of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we…

Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…

The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their…

In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…

In this paper, we present a formal quantification of epistemic uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due…

We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…

Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…

We study mathematical and computational models for computing the deformation of fiber-reinforced cross-plied laminates due to external forces. This requires an understanding of both micro-structural effects and different sources of…

The escape probability is a deterministic concept that quantifies some aspects of stochastic dynamics. This issue has been investigated previously for dynamical systems driven by Gaussian Brownian motions. The present work considers escape…

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the…

We introduce a general framework for analysing general probabilistic theories, which emphasises the distinction between the dynamical and probabilistic structures of a system. The dynamical structure is the set of pure states together with…

Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these…

A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…

This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are…

Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…