Related papers: Characteristic functions of measures on geometric …
We construct a canonical geometric rough path over $d$-dimensional tempered fractional Brownian motion (tfBm) for any Hurst parameter $H > 1/4$ and tempering parameter $\lambda > 0$. The main challenge stems from the non-homogeneous nature…
It has been recently shown that rough volatility models, where the volatility is driven by a fractional Brownian motion with small Hurst parameter, provide very relevant dynamics in order to reproduce the behavior of both historical and…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…
We prove an extension to the classical continuity theorem in rough paths. We show that two $p$-rough paths are close in all levels of iterated integrals provided the first $\lfl p \rfl$ terms are close in a uniform sense. Applications…
In this paper, in a multivariate setting we derive near optimal rates of convergence in the minimax sense for estimating partial derivatives of the mean function for functional data observed under a fixed synchronous design over H\"older…
Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…
We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After…
In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional It\^o formula…
The probabilistic symbol is the right-hand side derivative of the characteristic functions corresponding to the one-dimensional marginals of a stochastic process. This object, as long as the derivative exists, provides crucial information…
We introduce a notion of vague convergence for random marked metric measure spaces. Our main result shows that convergence of the moments of order $k \ge 1$ of a random marked metric measure space is sufficient to obtain its vague…
We aim to link random fields and marked point processes and therefore introduce a new class of stochastic processes which are defined on a random set in R^d. Unlike for random fields, the mark covariance function of a marked random set is…
The paper is split in two parts: in the first part, we construct the exact likelihood for a discretely observed rough differential equation, driven by a piecewise linear path. In the second part, we use this likelihood in order to construct…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
Getting tools that allow simple representations and comparisons of a set of categorical trajectories is of major interest for statisticians. Without loosing any information, we associate to each state a binary random indicator function,…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
We characterize probability measure with finite moment of any order in terms of the symmetric difference operators of their Fourier transforms. By using our new characterization, we prove the continuity $f(t,v)\in C((0, \infty),L^1_{2k-2…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
In this article, we discuss a probabilistic interpretation of McShane's identity as describing a finite measure on the space of embedded paths though a point.