相关论文: On the conditional distributions and the efficient…

In this paper we analyze a branching process with immigration defined recursively by $X_t=\theta_t\circ X_{t-1}+B_t$ for a sequence $(B_t)$ of i.i.d. random variables and random mappings $ \theta_t\circ x:=\theta_t(x)=\sum_{i=1}^xA_i^{(t)},…

In extreme value inference it is a fundamental problem how the target value is required to be extreme by the extreme value theory. In iid settings this study both theoretically and numerically compares tail estimators, which are based on…

In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\in (0,1)$. Random contractions appear naturally in insurance and…

We study the non-Gaussian tail of the curvature fluctuation, $\zeta$, in an inflationary scenario with a transient ultra slow-roll phase that generates a localized large enhancement of the spectrum of $\zeta$. To do so, we implement a…

We study the Tauberian relations between the moment generating function (MGF) and the complementary cumulative distribution function of a random variable whose MGF is finite only on part of the real line. We relate the right tail behavior…

This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…

We deduce in this short report the non-asymptotic for exponential tail of distribution for sums of independent centered random variables.

Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…

We study persistence probabilities for random walks in correlated Gaussian random environment first studied by Oshanin, Rosso and Schehr. From the persistence results, we can deduce properties of critical branching processes with offspring…

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…

The Generalized Pareto Distribution (GPD) plays a central role in modelling heavy tail phenomena in many applications. Applying the GPD to actual datasets however is a non-trivial task. One common way suggested in the literature to…

We study the extreme value statistics of the zero-average Gaussian free field (GFF) on random $r$-regular graphs and the Gaussian free field on $r$-regular trees. For random $r$-regular graphs of diverging size, for every fixed $r\ge3$, we…

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.

In the EFT of biased tracers the noise field $\varepsilon_g$ is not exactly uncorrelated with the nonlinear matter field $\delta$. Its correlation with $\delta$ is effectively captured by adding stochasticities to each bias coefficient. We…

We consider a Gaussian field $X = \{X_t, t \in T\}$ with values in a Banach space $B$ defined on a parametric set $T$ equal to $R^m$ or $Z^m.$ It is supposed that the distribution $\cal P$ of $X_t$ is independent of $t.$ We consider the…

Effective Field Theory (EFT) is an efficient method for parametrizing unknown high energy physics effects on low energy data. When applied to time-dependent backgrounds, EFT must be supplemented with initial conditions. In these…

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random…

We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned…

Large deviation theory and instanton calculus for stochastic systems are widely used to gain insight into the evolution and probability of rare events. At its core lies the realization that rare events are, under the right circumstances,…

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…