Related papers: Parametric inference and forecasting in continuous…
We introduce a novel modeling approach for time series imputation and forecasting, tailored to address the challenges often encountered in real-world data, such as irregular samples, missing data, or unaligned measurements from multiple…
Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…
Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally…
Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
We study local (also referred to as small-signal) stability of a network of identical DC/AC converters having a rotating degree of freedom. We develop a stability theory for a class of partitioned linear systems with symmetries that has…
We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…
We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…
This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient…
In this paper, we derive a general asymptotic implied volatility at the first-order for any stochastic volatility model using the heat kernel expansion on a Riemann manifold endowed with an Abelian connection. This formula is particularly…
Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…
We establish a notion of universality for the parabolic Anderson model via an invariance principle for a wide family of parabolic stochastic partial differential equations. We then use this invariance principle in order to provide an…
Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…
We study subexponential instability to characterize a dynamical instability of weak chaos. We show that a dynamical system with subexponential instability has an infinite invariant measure, and then we present the generalized Lyapunov…
We provide a detailed proof of Proposition 3.1 in the paper titled ``Backstepping control of a class of space-time-varying linear parabolic PDEs via time invariant kernel functions''. In the paper titled ``Backstepping control of a class of…
We introduce a multivariate stochastic volatility model for asset returns that imposes no restrictions to the structure of the volatility matrix and treats all its elements as functions of latent stochastic processes. When the number of…
In addition to providing high-profile successes in computer vision and natural language processing, neural networks also provide an emerging set of techniques for scientific problems. Such data-driven models, however, typically ignore…
In this paper, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler and Riemannian manifolds. A new and intrinsic proof of an important theorem in contraction analysis is given via the…
In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method needs not any cut-off procedures and…
Generative probabilistic forecasting produces future time series samples according to the conditional probability distribution given past time series observations. Such techniques are essential in risk-based decision-making and planning…