Related papers: Consistency of maximum likelihood estimation for s…
In this work we establish the posterior consistency for a parametrized family of partially observed, fully dominated Markov models. As a main assumption, we suppose that the prior distribution assigns positive probability to all…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for the stability in probability of stochastic dynamical systems with symmetries and…
A maximum likelihood type estimation of the drift and volatility coefficient parameters in the CIR type model driven by $\alpha$-stable noises is studied when the dispersion parameter $\varepsilon\to0$ and the discrete observations…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…
Nonlinear dynamical systems possessing an invariant subspace can display interesting dynamical behavior, such as on-off intermittency and bubbling. This letter shows that a class of such systems have amazing features of (1) supersensitivity…
We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…
We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems -- that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution. Using a hybrid…
This paper proposes several definitions of robust stability for logic dynamical systems (LDSs) with uncertain switching, including robust/uniform robust set stability and asymptotical (or infinitely convergent)/finite-time set stability…
Doubly robust estimators have gained widespread popularity in various fields due to their ability to provide unbiased estimates under model misspecification. However, the asymptotic theory for doubly robust estimators with continuous-time…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
Suppose we can choose from a set of linear autonomous systems with bounded process noise, the dynamics of each system are unknown, and we would like to design a stabilizing policy. The underlying question is how to estimate the dynamics of…
An attractor of a dynamical system may represent the system's 'desirable' state. Perturbations to the system may push the system out of the basin of attraction of the desirable attractor and into undesirable states. Hence, it is important…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…