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We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.
A necessary and sufficient condition is given for a subshift presentation to have a continuous $g$-function. An invariant necessary and sufficient condition is formulated for a subshift to posses a presentation that has a continuous…
We establish explicit socially optimal rules for an irreversible investment deci- sion with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic…
We construct a family of monotone and convex $C^1$ integro cubic splines under a strictly convex position of the dataset. Then, we find an optimal spline by considering its approximation properties. Finally, we give some examples to…
We investigate fundamental properties of adjoint functors to the precomposition functor in the category of strict polynomial functors.
We present equivalent conditions for a space $X$ with an unconditional basis to admit an equivalent norm with a strictly convex dual norm.
We prove a criterion that allows to construct units in product systems of correspondences with prescribed infinitesimal characterizations. This criterion summarizes proofs of known results and new applications. It also frees the hypothesis…
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
We derive axiomatically the probability function that should be used to make decisions given any form of underlying uncertainty.
The paper is split in two parts: in the first part, we construct the exact likelihood for a discretely observed rough differential equation, driven by a piecewise linear path. In the second part, we use this likelihood in order to construct…
We observe that if f is a continuous function on an interval I and x_0 \in I, then f is operator monotone if and only if the function (f(x) - f(x_0)/(x - x_0) is strongly operator convex. Then starting with an operator monotone function…
Motivated by applications requiring sparse or nonnegative controls, we investigate reachability properties of linear infinite-dimensional control problems under conic constraints. Relaxing the problem to convex constraints if the initial…
Given a set-valued stochastic process $(V_t)_{t=0}^T$, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors $\xi_t\in V_t$, admitting an equivalent martingale measure. The aim of this…
This note concerns the relationship between conditions on cost functions and domains and the convexity properties of potentials in optimal transportation and the continuity of the associated optimal mappings. In particular, we prove that if…
Let $C$ be a compact convex subset of $\mathbb{R}^n$, $f:C\to\mathbb{R}$ be a convex function, and $m\in\{1, 2, ..., \infty\}$. Assume that, along with $f$, we are given a family of polynomials satisfying Whitney's extension condition for…
In the past decade, we had developed a series of splitting contraction algorithms for separable convex optimization problems, at the root of the alternating direction method of multipliers. Convergence of these algorithms was studied under…
Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.