相关论文: Monotonicity and robustness in Wiener disorder det…

We consider certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance $\varepsilon ^2$. When $\varepsilon =0$ such equations have an unstable non-hyperbolic fixed point and the drift…

Gravitational instability in classical Jeans theory, General Relativity, and modified gravity is considered. The background density increase leads to a faster growth of perturbations in comparison with the standard theory. The transition to…

In this note, a Wegner estimate for random divergence-type operators that are monotone in the randomness is proven. The proof is based on a recently shown unique continuation estimate for the gradient and the ensuing eigenvalue liftings.…

We study a controlled version of the Bayesian sequential testing problem for the drift of a Wiener process, in which the observer exercises discretion over the signal intensity. This control incurs a running cost that reflects the resource…

We formulate and solve a variant of the quickest detection problem which features false negatives. A standard Brownian motion acquires a drift at an independent exponential random time which is not directly observable. Based on the…

We investigate in this work the spectrum of singularities of super-Brownian motion with stable branching. The main purpose is to provide a uniform description of the latter in high dimension $d\geq\tfrac{2}{\gamma-1}$, presenting the…

In this paper, we establish a universal variational characterization of the non-martingale components associated with weakly differentiable Wiener functionals in the sense of Le\~ao, Ohashi and Simas. It is shown that any Dirichlet process…

We study the effects of random positional disorder in the transmission of waves in a 1D Kronig-Penny model. For weak disorder we derive an analytical expression for the localization length and relate it to the transmission coefficient for…

We characterize throughout the spectral range of an optical trap the nature of the noise at play and the ergodic properties of the corresponding Brownian motion of an overdamped trapped single microsphere, comparing experimental, analytical…

We computationally study suspensions of slow and fast active Brownian particles that have undergone motility induced phase separation and are at steady state. Such mixtures, of varying non-zero activity, remain largely unexplored even…

The paper deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem…

This paper addresses the problems of stabilization, robust control, and observer design for nonlinear systems. We build upon recently a proposed method based on contraction theory and convex optimization, extending the class of systems to…

Machine learning models serve critical functions, such as classifying loan applicants as good or bad risks. Each model is trained under the assumption that the data used in training and in the field come from the same underlying unknown…

Although machine learning models typically experience a drop in performance on out-of-distribution data, accuracies on in- versus out-of-distribution data are widely observed to follow a single linear trend when evaluated across a testbed…

We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a…

A trained ML model is deployed on another `test' dataset where target feature values (labels) are unknown. Drift is distribution change between the training and deployment data, which is concerning if model performance changes. For a…

This dissertation examines the impact of a drift {\mu} on Brownian Bees, which is a type of branching Brownian motion that retains only the N closest particles to the origin. The selection effect in the 0-drift system ensures that it…

Consider the motion of a Brownian particle in three dimensions, whose two spatial coordinates are standard Brownian motions with zero drift, and the remaining (unknown) spatial coordinate is a standard Brownian motion with a non-zero drift.…

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…

The sliding friction of a dimer moving over a periodic substrate and subjected to an external force is studied in the steady state for arbitrary temperatures within a one-dimensional model. Nonlinear phenomena that emerge include dynamic…