arXiv subjects

Ekaterina Morozova

Publications and source records attributed to Ekaterina Morozova.

7 recordsLinked to original sources

arXiv2026

Nonparametric inference for density-dependent McKean--Vlasov diffusions

The present research is devoted to the nonparametric estimation of a density-dependent drift coefficient in a multivariate McKean--Vlasov diffusion from independent observations at a common time, as well as the stationary density. Under certain assumptions on the (known) potential, we reduce the problem to the one-dimensional one and construct a sieve maximum-likelihood estimator based on sparse ReQU neural networks subject to structural and Hölder constraints. Using the endpoint-adapted graded approximation, we achieve the rate of $\left(b_n\log n/n\right)^{2(β+1)/(2β+3)}$ for the Kullback-Leibler divergence between the true and estimated stationary densities, with $b_n$ being at most a logarithmic factor. Similarly, it is shown that the constructed estimator for the drift coefficient converges to the true one at the rate of $\left(b_n\log n/n\right)^{β/(2β+3)}$ in the $L^2$-metric. A matching Assouad lower bound proves minimax optimality of this bound up to logarithmic factors.

math.ST↗

arXiv2026

Density-Dependent McKean--Vlasov Diffusions: Subgaussian Occupancy Bounds and Polynomial Propagation of Chaos

We study the local density-dependent diffusion $dY_t=-Ξ(p_t(Y_t))\nablaΦ(Y_t)\,dt+\sqrt2\,dW_t$ and a clipped, randomly shifted histogram particle approximation on $\mathbb{R}^d$. The central difficulty is that the empirical density is evaluated at the particles' locations and re-enters their drift, while the confining force $\nablaΦ$ may be unbounded. We provide a path-space entropy proof under two verifiable analytic conditions: a uniform pointwise Gaussian envelope for the true density $p_t$, and a Gaussian--polynomial bound for its spatial gradient $\nabla p_t$. The potential is allowed to have a gradient of at most linear growth. The probabilistic input is a weighted exponential occupancy estimate under the independent product law. It is proved by Poissonizing the system at total intensity $N-1$, performing a one-cell leave-one-out estimate bounded via Poisson information, using Gaussian cell summability, and de-Poissonizing. For every fixed time horizon $T$, we obtain $\operatorname{Ent}(P_t^{N,k}|p_t^{\otimes k})\leq C_T k(h^2(1+|\log h|)+(h^{-d}+\log N)/N)$. Consequently, selecting the optimally balanced bandwidth $h\asymp (N\log N)^{-1/(d+2)}$ yields a total variation error of $\Vert P_t^{N,k}-p_t^{\otimes k}\Vert_{\operatorname{TV}}\leq C_T\sqrt{k}\,N^{-1/(d+2)}(\log N)^{d/[2(d+2)]}$ for fixed $k$. This includes the usual Ornstein--Uhlenbeck density and the density-dependent OU model whenever the PDE estimates hold on the considered interval. Furthermore, the histogram estimator offers a scalable approach for particle approximations. Using occupied-cell hashing, one algorithm step evaluates in expected $O(dLN)$ operations under standard constant-time hashing assumptions. For a fixed dimension and number of shifts, this requires expected $O(N)$ time, avoiding the $O(N^2)$ evaluation cost typical of standard kernel density estimators.

math.PR↗

arXiv2026

Ergodic Properties of Non-Linear Density-Dependent Perturbations of the Ornstein-Uhlenbeck Process

The present paper considers McKean-Vlasov SDEs with density-dependent spatially unbounded drift, which may be viewed as a non-linear density-dependent perturbation of the Ornstein-Uhlenbeck process. We develop a comprehensive theoretical framework for this class of equations. First, we establish strong well-posedness and derive optimal Gaussian pointwise bounds for both the solution density and its gradient. Then we derive an explicit expression for the stationary density and show that it satisfies logarithmic Sobolev and Poincaré inequalities. Finally, we prove exponential convergence to equilibrium in the $χ^2$-metric.

math.PR↗

arXiv2025

Decompounding Under General Mixing Distributions

This study focuses on statistical inference for compound models of the form $X=ξ_1+\ldots+ξ_N$, where $N$ is a random variable denoting the count of summands, which are independent and identically distributed (i.i.d.) random variables $ξ_1, ξ_2, \ldots$. The paper addresses the problem of reconstructing the distribution of $ξ$ from observed samples of $X$'s distribution, a process referred to as decompounding, with the assumption that $N$'s distribution is known. This work diverges from the conventional scope by not limiting $N$'s distribution to the Poisson type, thus embracing a broader context. We propose a nonparametric estimate for the density of $ξ$, derive its rates of convergence and prove that these rates are minimax optimal for suitable classes of distributions for $ξ$ and $N$. Finally, we illustrate the numerical performance of the algorithm on simulated examples.

math.ST↗

arXiv2024

Statistical Inference for Scale Mixture Models via Mellin Transform Approach

This paper deals with statistical inference for the scale mixture models. We study an estimation approach based on the Mellin -- Stieltjes transform that can be applied to both discrete and absolute continuous mixing distributions. The accuracy of the corresponding estimate is analysed in terms of its expected pointwise error. As an important technical result, we prove the analogue of the Berry -- Esseen inequality for the Mellin transforms. The proposed statistical approach is illustrated by numerical examples.

stat.ME↗

arXiv2022

Modelling the Bitcoin prices and the media attention to Bitcoin via the jump-type processes

In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the Lévy processes and is able to realistically reproduce the jump-type dynamics of the considered time series. We focus on the low-frequency setup, which is for the Lévy - based models essentially more difficult than the high-frequency case. We design a semiparametric estimation procedure for the statistical inference on the parameters and the Lévy measures of the considered processes. We show that the dynamics of the market attention can be effectively modelled by the Lévy processes with finite Lévy measures, and propose a data-driven procedure for the description of the Bitcoin prices.

q-fin.ST↗

arXiv2021

Extreme value analysis for mixture models with heavy-tailed impurity

This paper deals with the extreme value analysis for the triangular arrays, which appear when some parameters of the mixture model vary as the number of observations grow. When the mixing parameter is small, it is natural to associate one of the components with "an impurity" (in case of regularly varying distribution, "heavy-tailed impurity"), which "pollutes" another component. We show that the set of possible limit distributions is much more diverse than in the classical Fisher-Tippett-Gnedenko theorem, and provide the numerical examples showing the efficiency of the proposed model for studying the maximal values of the stock returns.

math.ST↗