Related papers: Set-valued mapping and Rough Probability
Driven by applications in telecommunication networks, we explore the simulation task of estimating rare event probabilities for tandem queues in their steady state. Existing literature has recognized that importance sampling methods can be…
Rough stochastic differential equations (RSDEs) are common generalisations of Ito SDEs and Lyons RDEs and have emerged as new tool in several areas of applied probability, including non-linear stochastic filtering, pathwise stochastic…
This paper provides a detailed introductory description of Subset Simulation, an advanced stochastic simulation method for estimation of small probabilities of rare failure events. A simple and intuitive derivation of the method is given…
One the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility…
This paper is a case study of probabilistic approach to homological aspects of topological quantum field theory via the example of topological quantum mechanics. We propose topological correlations in terms of large variance limit. An…
We investigate the distribution of the well-studied Shapley--Shubik values in weighted voting games where the agents are stochastically determined. The Shapley--Shubik value measures the voting power of an agent, in typical collective…
Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…
Annealed functional CLT in the rough path topology is proved for the standard class of ballistic random walks in random environment. Moreover, the `area anomaly', i.e. a deterministic linear correction for the second level iterated integral…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
To give characterizations of monotonically countably paracompact spaces with set-valued maps, Yamazaki [22] introduced the notion of strictly increasing closed cover of a topological space with which the boundedness of a set-valued map was…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…
In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is…
New in the probability theory and eventology theory, the concept of Kopula (eventological copula) is introduced. The theorem on the characterization of the sets of events by Kopula is proved, which serves as the eventological pre-image of…
Our goal is to build robust optimization problems for making decisions based on complex data from the past. In robust optimization (RO) generally, the goal is to create a policy for decision-making that is robust to our uncertainty about…
Local stochastic volatility refers to a popular model class in applied mathematical finance that allows for "calibration-on-the-fly", typically via a particle method, derived from a formal McKean-Vlasov equation. Well-posedness of this…
We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter $H < 1/2$. This regime recently attracted a lot of attention both from the statistical and…
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…
In the classical probability in continuous random variables there is no distinguishing between the probability involving strict inequality and non strict inequality. Moreover a probability involves equality collapse to zero without…
Given a stream of Bernoulli random variables, consider the problem of estimating the mean of the random variable within a specified relative error with a specified probability of failure. Until now, the Gamma Bernoulli Approximation Scheme…