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In the thesis at hand we give a comprehensive discussion of basic problems for generalized Maxwell equations with mixed boundary conditions using the calculus of alternating differential forms on Riemannian manifolds of arbitrary dimension.…
This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance:…
Let $\mathcal{M}^{\mathrm{st}}$ ($\mathcal{M}^{\mathrm{pst}}$) be a moduli space of stable (polystable) bundles with fixed determinant on a complex surface with $b_1=1$, $p_g=0$, and let $Z\subset \mathcal{M}^{\mathrm{st}}$ be a pure…
Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energy condition. For manifolds with smooth boundary, this is…
We provide sharp bounds for the supremum of countably many stochastic convolutions taking values in a 2-smooth Banach space. As a consequence, we obtain sharp bounds on the modulus of continuity of a family of stochastic integrals indexed…
Methodologies to test hypotheses about the tail-heaviness of an underlying distribution are introduced based on results of Rojo (1996) using the limiting behavior of the extreme spacings. The tests are consistent and have point-wise robust…
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…
We study how iterated convolutions of probability measures compare under stochastic domination. We give necessary and sufficient conditions for the existence of an integer $n$ such that $\mu^{*n}$ is stochastically dominated by $\nu^{*n}$…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
In this paper we present two different results in the context of nonlinear analysis. The first one is essentially a nonlinear technique that, in view of its strong generality, may be useful in different practical problems. The second…
By using a classical truncated argument and introducing the local Wasserstein distance, the global existence and uniqueness are proved for the distribution dependent SDEs with local Lipschitz coefficients. Due to the measure dependence, the…
A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…
In this article, we first introduce the notion of a {\it continuous cover} of a manifold parametrised by any compact manifold endowed with a mass 1 volume-form. We prove that any such cover admits a partition of unity where the usual sum is…
In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point…
Measure rigidity is a branch of ergodic theory that has recently contributed to the solution of some fundamental problems in number theory and mathematical physics. Examples are proofs of quantitative versions of the Oppenheim conjecture,…
This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…
The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk…
In this work we establish the posterior consistency for a parametrized family of partially observed, fully dominated Markov models. As a main assumption, we suppose that the prior distribution assigns positive probability to all…
This work addresses the question of regularity of solutions to evolutionary (quasi-static and dynamic) perfect plasticity models. Under the assumption that the elasticity set is a compact convex subset of deviatoric matrices, with $C^2$…
This chapter examines how positivity and order play out in two important questions in mathematical economics, and in so doing, subjects the postulates of continuity, additivity and monotonicity to closer scrutiny. Two sets of results are…