Related papers: Estimating a class of diffusions from discrete obs…
We study a symmetric diffusion $X$ on $\mathbb{R}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients $a^\omega$. The diffusion is formally associated with $L^\omega u =…
Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of…
In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general…
We study the problem of parameters estimation in Indirect Observability contexts, where $X_t \in R^r$ is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an…
The paper deals with the fast-slow motions setups in the continuous time $\frac {dX^\ve(t)}{dt}=\frac 1\ve\sig(X^\ve(t))\xi(t/\ve^2)+b(X^\ve(t)),\, t\in [0,T]$ and the discrete time…
We investigate the approximation and estimation rates of conditional diffusion transformers (DiTs) with classifier-free guidance. We present a comprehensive analysis for ``in-context'' conditional DiTs under four common data assumptions. We…
Multidimensional hypoelliptic diffusions arise naturally in different fields, for example to model neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. In this paper we…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
We study the problem of parameter estimation for a univariate discretely observed ergodic diffusion process given as a solution to a stochastic differential equation. The estimation procedure we propose consists of two steps. In the first…
We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…
Diffusion models, typically formulated as discretizations of stochastic differential equations (SDEs), have achieved state-of-the-art performance in generative tasks. However, their theoretical analysis often involves complex proofs. In…
The paper considers an Euler discretization based numerical scheme for approximating functionals of invariant distribution of an ergodic diffusion. Convergence of the numerical scheme is shown for suitably chosen discretization step, and a…
We assume that we observe $N$ independent copies of a diffusion process on a time-interval $[0,2T]$. For a given time $t$, we estimate the transition density $p_t(x,y)$, namely the conditional density of $X_{t + s}$ given $X_s = x$, under…
According to a theorem of S. Schumacher, for a diffusion X in an environment determined by a stable process that belongs to an appropriate class and has index a, it holds that X_t/(log t)^a converges in distribution, as t goes to infinity,…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
For a class of (non-symmetric) diffusion processes on a length space, which in particular include the (reflecting) diffusion processes on a connected compact Riemannian manifold, the exact convergence rate is derived for $({\mathbb E}…
We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of…
Modeling information spread through a network is one of the key problems of network analysis, with applications in a wide array of areas such as marketing and public health. Most approaches assume that the spread is governed by some…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance…