arXiv research

The paper improves PAC-Bayes bounds for losses with finite moments.

The paper proves that Gaussian field critical points have finite moments.

Unified framework for mean testing under truncation bias.

We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten DCC-GARCH models as nonlinear Markov chains. Moreover, we study the existence of their f…

New algorithm for robust regression with subgaussian error bound.

In linear stochastic bandits, it is commonly assumed that payoffs are with sub-Gaussian noises. In this paper, under a weaker assumption on noises, we study the problem of \underline{lin}ear stochastic {\underline b}andits with h{\underline e}avy-{\underline t}ailed payoffs (LinBET), where the distributions have finite…

We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previ…

This paper investigates analytic properties of American option prices under the finite moment log-stable (FMLS) model. Under this model the price of American options is characterised by the free boundary problem of a fractional partial differential equation (FPDE) system. Using the technique of approximation we prove t…

We establish an explicit pricing formula for the class of Lévy-stable models with maximal negative asymmetry (Log-Lévy model with finite moments and stability parameter $1<α\leq 2$) in the form of rapidly converging series. The series is obtained with help of Mellin transform and the residue theory in $\mathbb{C}^2$. T…

New margin-based learning guarantees improve generalization bounds.

The study of random walks on hyperbolic spaces and Teichmüller spaces, proving central limit theorems and geodesic tracking.

Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require ergodicity in order establish consistency and asymptotic normality of the associat…

In this paper we study the exponential functionals of the processes $X$ with independent increments , namely $I_t= \int _0^t\exp(-X_s)ds, _,\,\, t\geq 0,$ and also $I_{\infty}= \int _0^{\infty}\exp(-X_s)ds.$ When $X$ is a semi-martingale with absolutely continuous characteristics, we derive recurrent integral equat…

New protocols show 1-bit mean estimation can be order-optimal without interaction.

Study on queues with Hawkes arrivals, proving steady-state behavior and developing an efficient algorithm.

A new law limits kurtosis contrast in balanced mixtures.

In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at …

Variational inference with α-divergences has been widely used in modern probabilistic machine learning. Compared to Kullback-Leibler (KL) divergence, a major advantage of using α-divergences (with positive α values) is their mass-covering property. However, estimating and optimizing α-divergences require to use importa…

Improved KL bounds and Wasserstein guarantees for diffusion flow matching under minimal conditions.

Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.

We study the estimation of the parametric components of single and multiple index volatility models. Using the first- and second-order Stein's identities, we develop methods that are applicable for the estimation of the variance index in the high-dimensional setting requiring finite moment condition, which allows for h…

High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following properties: (i) They are not Gaussian and their center is well adjusted by Levy dist…

We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of estimators that achieve sub-Gaussian type deviations even for heavy tailed data. We revisit some of these estimators through the lens of differ…

New robust estimators achieve subgaussian bounds using VC-dimension.

In this paper, for $μ$ and $ν$ two probability measures on $\mathbb{R}^d$ with finite moments of order $ρ\ge 1$, we define the respective projections for the $W_ρ$-Wasserstein distance of $μ$ and $ν$ on the sets of probability measures dominated by $ν$ and of probability measures larger than $μ$ in the convex order. Th…

Proposes a new ARCH framework for Hilbert space data.

The paper improves Monte Carlo methods for optimization problems.

New method improves generative modeling on convex domains using regularized mirror maps and Student-t priors.

New method finds closest martingale to Brownian motion.

Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we establish a new framework that generalizes distance correlation --- a correlation mea…

The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important difference is that the population covariance matrices, which are assumed to be non-random…

The COS method for European options pricing is improved with a new bound for the number of terms.

BBVI converges nearly dimensionally independent for log-concave targets.

Study uses Wasserstein distance to identify causal orders and unmix sources.

In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, $W_t = B_t + μt, t\geq 0,$ where $(B_t)$ is a standard Brownian motion. Truncated variation differs from regular variation by neglect…

A new method for estimating causal parameters from observables reduces the need for finite moment conditions.

New method makes reinforcement learning robust to heavy-tailed rewards.

Develops a contraction framework for MCMC mixing rates.

This paper shows universality in spectrum behavior for random inner-product kernel matrices in polynomial regime.

Improved portfolio optimization method reduces risk and improves performance.

Paper introduces robust kernel ridge regression using Cauchy loss for handling various noise types.

This note presents an operational measure of fat-tailedness for univariate probability distributions, in $[0,1]$ where 0 is maximally thin-tailed (Gaussian) and 1 is maximally fat-tailed. Among others,1) it helps assess the sample size needed to establish a comparative $n$ needed for statistical significance, 2) allows…

New diffusion models learn distributions from samples with improved error bounds.

We derive a new radial link for binary classification under shared elliptical distributions.