Related papers: Discrete time pontryagin principles in banach spac…
In this paper, we consider a varying terminal time structure for the stochastic optimal control problem under state constraints, in which the terminal time varies with the mean value of the state. In this new stochastic optimal control…
A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic…
In this paper we investigate the power instability properties and give necessary and sufficient conditions for the concepts of uniform power instability, power instability and strong power instability for linear discrete-time system…
Variational interpolants are an indispensable tool for the construction of gradient-flow solutions via the Minimizing Movement Scheme. The De Giorgi lemma provides the associated discrete energy-dissipation inequality. It was originally…
In this paper, we extend the Banach contraction principle to metric-like as well as partial metric spaces (not essentially complete) equipped with an arbitrary binary relation. Thereafter, we derive some fixed point results which are…
Versions of the Oseledets multiplicative ergodic theorem for cocycles acting on infinite-dimensional Banach spaces have been investigated since the pioneering work of Ruelle in 1982 and are a topic of continuing research interest. For a…
In this paper we defined some function spaces on time scale which are Banach spaces respect to supremum norm. We study integral transformations which are carry to some important properties between mentioned above function spaces.
We provide a method for constructing (possibly non-trivial) measures on non-locally compact Polish subspaces of infinite-dimensional separable Banach spaces which, under suitable assumptions, are minimizers of causal variational principles…
In this paper we extend vessel theory, or equivalently, the theory of overdetermined $2D$ systems to the Pontryagin space setting. We focus on realization theorems of the various characteristic functions associated to such vessels. In…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
A general device is proposed, which provides for extension of exponential inequalities for sums of independent real-valued random variables to those for martingales in the 2-smooth Banach spaces. This is used to obtain optimum bounds of the…
We investigate intrinsic Baire classes of Banach spaces defined by Argyros, Godefroy and Rosenthal (2003). We introduce a construction, for any Banach space $X$ with a basis, of an $\ell_1$-saturated separable Banach space $Y$ such that for…
In this paper, first we present a new useful way of formulating probabilistic normed spaces. Then by using this formulation and probabilistic normed space version of the Baire category theorem, we prove four important results of functional…
We provide an improvement of the maximum principle of Pontryagin of the Optimal Control problems. We establish differentiability properties of the value function of problems of Optimal Control with assumptions as low as possible. Notably,…
This paper focuses on infinite-horizon optimal control problems for dissipative systems and the relations to their finite-horizon formulations. We show that, for a large class of problems, dissipativity of the state equation, when a…
The famous Banach Contraction Principle holds in complete metric spaces, but completeness is not a necessary condition -- there are incomplete metric spaces on which every contraction has a fixed point. The aim of this paper is to present…
Through the Pontryagin maximum principle, we solve a minimal-time problem for a linear control system on a cylinder, considered as a homogeneous space of the solvable Lie group of dimension two. The main result explicitly shows the…
A mathematical framework is developed for the analysis of causal fermion systems in the infinite-dimensional setting. It is shown that the regular spacetime point operators form a Banach manifold endowed with a canonical Fr\'echet-smooth…
In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control problems in the Wasserstein space of probability measures. The dynamics, is described by a transport equation with non-local velocities and is subject to…
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…