相关论文: Expectation, Conditional Expectation and Martingal…
The paper explores the concept of the \emph{expectile risk measure} within the framework of the Fundamental Risk Quadrangle (FRQ) theory. According to the FRQ theory, a quadrangle comprises four stochastic functions associated with a random…
We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract…
The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
{Consider a c\`adl\`ag local martingale $M$ with square brackets $[M]$. In this paper, we provide upper and lower bounds for expectations of the type ${\mathbb E} [M]^{q/2}_{\tau}$, for any stopping time $\tau$ and $q\ge 2$, in terms of…
In this paper, we show that the conditional expectation of a random variable with finite second moment given a $\sigma$-algebra is the unique critical point of an energy functional in Hilbert space $L^2$. Then, we extend by density the…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…
We obtain a necessary and sufficient condition for the orthomartingale-coboundary decomposition. We establish a sufficient condition for the approximation of the partial sums of a strictly stationary random fields by those of stationary…
A strict local martingale is a local martingale that is not a martingale. We investigate how such a process might arise from a true martingale as a result of an enlargement of the filtration. We study and implement a particular type of…
In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
For a real Borel measurable function b, which satisfies certain integrability conditions, it is possible to define a stochastic integral of the process b(Y) with respect to a Brownian motion W, where Y is a diffusion driven by W. It is well…
In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and…
For a given element $f\in L^1$ and a convex cone $C\subset L^\infty$, $C\cap L^\infty_+=\{0\}$ we give necessary and sufficient conditions for the existence of an element $g\ge f$ lying in the polar of $C$. This polar is taken in…
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
This paper introduces Martingales by covering introductory measure theory concepts and the Lebesgue Integration and Conditional Expectation. It follows up with proofs of Kolomorgov's Theorem on conditional expectations, the Martingale…
We prove a martingale-coboundary representation for random fields with a completely commuting filtration. For random variables in L2 we present a necessary and sufficient condition which is a generalization of Heyde's condition for one…