Related papers: Assigning probabilities to non-Lipschitz mechanica…
The Dirichlet forms methods, in order to represent errors and their propagation, are particularly powerful in infinite dimensional problems such as models involving stochastic analysis encountered in finance or physics, cf. [5]. Now, coming…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
We develop the fundamental theorem of asset pricing in a probability-free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then…
We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau-Lifshitz-Gilbert equation in $\mathbb{R}^2$. Our characterization yields a partially regular solution, smooth away from a…
We propose a family of "exactly solvable" probability distributions to approximate partition functions of two-dimensional statistical mechanics models. While these distributions lie strictly outside the mean-field framework, their free…
In this article we will study the initial value problem for some Schr\"odinger equations with Diraclike initial data and therefore with infinite L2 mass, obtaining positive results for subcritical nonlinearities. In the critical case and in…
The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…
The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…
We derive exponential bounds on probabilities of large deviations for "light tail" martingales taking values in finite-dimensional normed spaces. Our primary emphasis is on the case where the bounds are dimension-independent or nearly so.…
The initial-boundary value problem for an infinite one-dimensional chain of harmonic oscillators on the half-line is considered. The large time asymptotic behavior of solutions is studied. The initial data of the system are supposed to be a…
We deal with homogeneous Dirichlet and Neumann boundary-value problems for anisotropic elliptic operators of p-Laplace type. They emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly…
We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a…
We consider the Lipschitz continuous dependence of solutions for the Novikov equation with respect to the initial data. In particular, we construct a Finsler type optimal transport metric which renders the solution map Lipschitz continuous…
The stability theory for hyperbolic initial boundary value problems relies most of the time on the Laplace transform with respect to the time variable. For technical reasons, this usually restricts the validity of stability estimates to the…
We extend the classic convergence rate theory for subgradient methods to apply to non-Lipschitz functions. For the deterministic projected subgradient method, we present a global $O(1/\sqrt{T})$ convergence rate for any convex function…
This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random polynomials whose coefficients are independently and identically distributed as…
The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…
In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating Robin boundary condition. We establish the qualitative homogenization theorem on any Lipschitz domains satisfying a non-resonance…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…