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We study functional stochastic differential equations with a locally unbounded, functional drift focusing on well-posedness, stability and the strong Feller property. Following the non-functional case, we only consider integrability…
While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also non-linear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali this…
We consider the dynamics of the stochastic shadow Gierer-Meinhardt system with one-dimensional standard Brownian motion. We establish the global existence and uniqueness of solutions. We also prove a large deviation result.
As machine learning models become increasingly prevalent in critical decision-making models and systems in fields like finance, healthcare, etc., ensuring their robustness against adversarial attacks and changes in the input data is…
This paper studies the problem of robustly learning the correlation function for a univariate time series with the presence of noise, outliers and missing entries. The outliers or anomalies considered here are sparse and rare events that…
Our investigation is specially motivated by the stochastic version of a common model of potential spread in a dendritic tree. We do not assume the noise in the junction points to be Markovian. In fact, we allow for long-range dependence in…
Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…
In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong…
Circular variables that represent directions or periodic observations arise in many fields, such as biology and environmental sciences. An important issue when dealing with circular data is how to estimate their dispersion robustly,…
An extensive numerical analysis of the scattering and transport properties of the power-law banded random matrix model (PBRM) at criticality in the presence of orthogonal, unitary, and symplectic symmetries is presented. Our results show a…
Using monotonicity theory we investigate the continuous dependence on parameters for the discrete BVPs which can be written in a form of a nonlinear system.
We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is…
Changes, planned or unexpected, are common during the execution of real-life processes. Detecting these changes is a must for optimizing the performance of organizations running such processes. Most of the algorithms present in the…
Two cases of a phenomenological model for ferromagnetism are considered, discrete and continuous. And the relationship, in general, between discrete and continuous models explored. In a similar way to the logistic map behavior, the…
The effect of a drift term in the presence of fixed boundaries is studied for the one-dimensional Edwards-Wilkinson equation, to reveal a general mechanism that causes a change of exponents for a very broad class of growth processes. This…
We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized…
In deep learning applications, robustness measures the ability of neural models that handle slight changes in input data, which could lead to potential safety hazards, especially in safety-critical applications. Pre-deployment assessment of…
The paper is devoted to the problem of resonances in one-dimensional disordered systems. Some of the previous results are reviewed and a number of new ones is presented. These results pertain to different models (continuous as well as…
We identify complete monotonicity properties underlying a variety of well-known sharp Strichartz inequalities in euclidean space.
In this note, we study monotone dynamical systems with respect to polyhedral cones. Using the half-space representation and the vertex representation, we propose three equivalent conditions to certify monotonicity of a dynamical system with…