Related papers: Stochastic measure distortions induced by quantile…

We develop a novel approach for the construction of quantile processes governing the stochastic dynamics of quantiles in continuous time. Two classes of quantile diffusions are identified: the first, which we largely focus on, features a…

In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($\Delta$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes…

We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are…

When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable…

Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…

Distorted distributions were introduced in the context of actuarial science for several variety of insurance problems. In this paper we consider the quantile-based probabilistic mean value theorem given in Di Crescenzo et al. [4] and…

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…

The outcomes of a series of measurements, made on a quantum system, form a sequence of random events which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network…

Building on recent developments in models focused on the shape properties of odds ratios, this paper introduces two new models that expand the class of available distributions while preserving specific shape characteristics of an underlying…

This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main features are that they measure risk of processes that are functions of the history of a base…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…

The Shapley value provides a principled framework for fairly distributing rewards among participants according to their individual contributions. While prior work has applied this concept to data valuation in machine learning, existing…

Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…

A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…

We introduce the concept of forward rank-dependent performance processes, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of…

Stochastic simulation has been widely used to analyze the performance of complex stochastic systems and facilitate decision making in those systems. Stochastic simulation is driven by the input model, which is a collection of probability…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…