Related papers: Vector-valued Almost Sure Invariance Principle For…
This paper addresses invariance principles for a certain class of switched nonlinear systems. We provide an extension of LaSalle's Invariance Principle for these systems and state asymptotic stability criteria. We also present some related…
We prove a fiberwise almost sure invariance principle for random piecewise expanding transformations in one and higher dimensions using recent developments on martingale techniques.
Several studies analyzed certain nonlinear dynamical systems by showing that the cyclic number of sign variations in the vector of derivatives is an integer-valued Lyapunov function. These results are based on direct analysis of the…
In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
In this paper, we consider the convergence rate with respect to the Wasserstein distance in the invariance principle for sequential dynamical systems. We utilize and modify the techniques previously employed for stationary sequences to…
We present a novel generic framework to approximate the non-equilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the…
Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally…
We prove the almost sure invariance principle with rate $o(n^{\varepsilon})$ for every $\varepsilon > 0$ for H\"older continuous observables on nonuniformly expanding and nonuniformly hyperbolic transformations with exponential tails.…
A new Small-Gain Theorem is presented for general nonlinear control systems. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability and input-to-state…
We give sufficient Gordin-type criteria for the iterated (enhanced) weak invariance principle to hold for deterministic dynamical systems. Such an invariance principle is intrinsically related to the interpretation of stochastic integrals.…
We prove the one-dimensional almost sure invariance principle with essentially optimal rates for slowly (polynomially) mixing deterministic dynamical systems, such as Pomeau-Manneville intermittent maps, with H\"older continuous…
Approximate Message Passing (AMP), originally designed to solve high-dimensional linear inverse problems, has found broad applications in signal processing and statistical inference. Among its key variants, Vector Approximate Message…
In this paper we introduce a class of non uniformly expanding random dynamical system with additive noise and we prove a BV estimate between the stationary measure and the quasistationary measure of the system. Furthermore, we use these…
We propose VISP: Volatility Informed Stochastic Projection, an adaptive regularization method that leverages gradient volatility to guide stochastic noise injection in deep neural networks. Unlike conventional techniques that apply uniform…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
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…
A vector variational principle is proved.
This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…
Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly…