Related papers: Most probable paths for developed processes
We investigate the asymptotic behavior of the maximum likelihood estimators of the unknown parameters of positive recurrent Ornstein-Uhlenbeck processes driven by Ornstein-Uhlenbeck processes.
Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of…
The probability of trajectories of weakly diffusive processes to remain in the tubular neighbourhood of a smooth path is given by the Freidlin-Wentzell-Graham theory of large deviations. The most probable path between two states (the…
This paper considers a classical question of approximation of Brownian motion by a random walk in the setting of a sub-Riemannian manifold $M$. To construct such a random walk we first address several issues related to the degeneracy of…
It is well known that between all processes with independent increments, essentially only the Brownian motion and the Poisson process possess the chaotic representation property (CRP). Thus, a natural question appears: What is an…
Malliavin Calculus can be seen as a differential calculus on Wiener spaces. We present the notion of stochastic manifold for which the Malliavin Calculus plays the same role as the classical differential calculus for the differential…
In this paper, we investigate a deep learning method for predicting path-dependent processes based on discretely observed historical information. This method is implemented by considering the prediction as a nonparametric regression and…
We consider the problem of efficient estimation of the drift parameter of an Ornstein-Uhlenbeck type process driven by a L\'{e}vy process when high-frequency observations are given. The estimator is constructed from the time-continuous…
In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. The coefficients that are obtained from the expansion of Brownian motion in this polynomial basis are…
This paper presents a novel on-line path planning method that enables aerial robots to interact with surfaces. We present a solution to the problem of finding trajectories that drive a robot towards a surface and move along it. Triangular…
We consider a reflected Ornstein-Uhlenbeck process $X$ driven by a fractional Brownian motion with Hurst parameter $H\in (0, \frac12) \cup (\frac12, 1)$. Our goal is to estimate an unknown drift parameter $\alpha\in (-\infty,\infty)$ on the…
The dynamics of mechanical systems such as turbomachinery with multiple blades are often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibrational modes, and…
We consider the problem of choosing the optimal (in the sense of mean-squared prediction error) multistep predictor for an autoregressive (AR) process of finite but unknown order. If a working AR model (which is possibly misspecified) is…
We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…
In this paper, we consider the problem of minimizing a smooth function on a Riemannian manifold and present a Riemannian gradient method with momentum. The proposed algorithm represents a substantial and nontrivial extension of a recently…
Variational approaches to data assimilation, and weakly constrained four dimensional variation (WC-4DVar) in particular, are important in the geosciences but also in other communities (often under different names). The cost functions and…
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…
We present an iterative sampling method which delivers upper and lower bounding processes for the Brownian path. We develop such processes with particular emphasis on being able to unbiasedly simulate them on a personal computer. The…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…
We study a class of martingale inequalities involving the running maximum process. They are derived from pathwise inequalities introduced by Henry_Labordere et al. (2013) and provide an upper bound on the expectation of a function of the…