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Publications associées (132)
Detecting whether a stochastic process is finitely expressed in a basis
Victor Panaretos, Neda Mohammadi Jouzdani
Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2023Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures
This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Va ...
New York2023Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective
Victor Panaretos, Neda Mohammadi Jouzdani
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...
Amsterdam2023Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs
Robert Dalang, Carsten Hao Ye Chong
We consider a class of parabolic stochastic PDEs on bounded domains D c Rd that includes the stochastic heat equation but with a fractional power gamma of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces ...
INT STATISTICAL INST2023Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equations
Giancarlo Ferrari Trecate, Luca Furieri, Clara Lucía Galimberti, Daniele Martinelli
In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of recently introduced Rec ...
New York2023The exploration process of critical Boltzmann planar maps decorated by a triangular O(n) loop model
In this paper we investigate pointed (q, g, n)-Boltzmann loop-decorated maps with loops traversing only inner triangular faces. Using peeling exploration Budd (2018) modified to this setting we show that its law in the non-generic critical phase can be cod ...
IMPA2022