Related papers: Martingale estimation functions for Bessel process…
In this paper, we present a novel methodology to perform Bayesian inference for Cox processes in which the intensity function is driven by a diffusion process. The novelty lies in the fact that no discretization error is involved, despite…
In this paper, we consider functionals based on moments and non-linear entropies which have a linear growth in time in case of source-type so-lutions to the fast diffusion or porous medium equations, that are also known as Barenblatt…
In this paper we develop statistical inference tools for high dimensional functional time series. We introduce a new concept of physical dependent processes in the space of square integrable functions, which adopts the idea of basis…
The interpretation of cosmological observables requires the use of increasingly sophisticated theoretical models. Since these models are becoming computationally very expensive and display non-trivial uncertainties, the use of standard…
A new stochastic process is introduced and considered - squared Bessel process with special stochastic time. The analogues of fundamental properties for Brownian motion are deduced for squared Bessel process. In particular an analogue of…
We propose an unbiased Monte-Carlo estimator for $\mathbb{E}[g(X_{t_1}, \cdots, X_{t_n})]$, where $X$ is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a…
We study upper estimates of the martingale dimension $d_m$ of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that $d_m=1$…
We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators. In order to select proper initial values for…
A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…
In this paper we present a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism. The procedure is applied to studies of the double longitudinal spin asymmetry in…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
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…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
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…
Neural diffusion processes provide a scalable, non-Gaussian approach to modelling distributions over functions, but existing formulations are limited to single-task inference and do not capture dependencies across related tasks. In many…
The dissipation of general convex entropies for continuous time Markov processes can be described in terms of backward martingales with respect to the tail filtration. The relative entropy is the expected value of a backward submartingale.…
We report on a versatile method to compensate the linear attenuation in a medium, independently of its microscopic origin. The method exploits diffraction-limited Bessel beams and tailored on-axis intensity profiles which are generated…
We investigate the effects of noise reinforcement on a Bessel process of dimension $d\in(0,2)$, and more specifically on the asymptotic behavior of its additive functionals. This leads us to introduce a local time process and its inverse.…
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel…
This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…