Related papers: A representation theorem for set-valued submarting…

Let (f_n) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (d_n) from [0,1]^n such that int_0^1 d_n(x_1,...,x_n) dx_n = 0 for almost all x_1,...,x_{n-1}, and such that the law of (f_n) is the same…

In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…

The article is devoted to the integration order replacement technique for iterated Ito stochastic integrals and iterated stochastic integrals with respect to martingales. We consider the class of iterated Ito stochastic integrals, for which…

In this paper we investigate sublinear semigroups whose pointwise generators are given by non-local Hamilton-Jacobi-Bellman operators. Our main result provides a stochastic representation in terms of a family of sublinear (conditional)…

We formulate a class of singular integral operators in arbitrarily many parameters using mixed type characterizing conditions. We also prove a multi-parameter representation theorem saying that a general operator in our class can be…

Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational…

This paper investigates best-worst choice probabilities (picking the best and the worst alternative from an offered set). It is shown that non-negativity of best-worst Block-Marschak polynomials is necessary and sufficient for the existence…

A recently proposed integral representation for permanents is rederived using only elementary combinatorics. For this proof the assumption that the matrix, for which the permanent is calculated, has an inverse is not necessary.

Suppose that $X_1, \ldots , X_n$ are continuous semimartingales that are reversible and have nondegenerate crossings. Then the corresponding rank processes can be represented by generalized Stratonovich integrals, and this representation…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on a locally convex space $\Phi$. Our construction of the stochastic integral is based on the theory of tensor products…

This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…

The paper proposes a novel technique for representing templates and instances of concept classes. A template representation refers to the generic representation that captures the characteristics of an entire class. The proposed technique…

We show that all local martingales with respect to the initially enlarged natural filtration of a vector of multivariate point processes can be weakly represented up to the minimum among the explosion times of the components. We also prove…

The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify…

Let $X$ be a point process and let $\mathbb{X}$ denote the filtration generated by $X$. In this paper we study martingale representation theorems in the filtration $\mathbb{G}$ obtained as an initial and progressive enlargement of the…

The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…

Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the…