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Concept

Stochastic calculus

Related publications (25)

Transportation-based functional ANOVA and PCA for covariance operators

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Inst Mathematical Statistics-Ims2024

Static and Dynamic Stochastic Analysis of a Temperature-Sensitive VO2 Spiking Neuron

Mihai Adrian Ionescu, Teodor Rosca

In this work, we investigate the intrinsic cycle-to-cycle variations in a spiking temperature-sensitive neuron, based on the resistive switching of a Vanadium dioxide (VO2) two-terminal device. We study how this phenomenon impacts the spike rate jitter, an ...

IEEE2023

Functional data analysis with rough sample paths?

Victor Panaretos, Neda Mohammadi Jouzdani

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

TAYLOR & FRANCIS LTD2024

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 SCIENCE2023

Tensor approximation of the self-diffusion matrix of tagged particle processes

Christoph Max Strössner

The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of de ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

Event-driven acquisition for content-enriched microscopy

Suliana Manley, Dora Mahecic, Martin Weigert, Juliette Griffie, Chen Zhang, Willi Leopold Stepp

Event-driven acquisition uses neural-network-based recognition of specific biological events to trigger switching between slow and fast super-resolution imaging, enriching the capture of interesting events with high spatiotemporal resolution. A common goal ...

Nature Publishing Group2022

The Completion Of Covariance Kernels

Victor Panaretos, Kartik Waghmare

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...

INST MATHEMATICAL STATISTICS-IMS2022

Reinforcement Learning for the occupant-centric operation of building energy systems: Theoretical and experimental investigations

Amirreza Heidari

Occupant behavior, defined as the presence and energy-related actions of occupants, is today known as a key driver of building energy use. Closing the gap between what is provided by building energy systems and what is actually needed by occupants requires ...

EPFL2022

STEPS 4.0: Fast and memory-efficient molecular simulations of neurons at the nanoscale

Felix Schürmann, James Gonzalo King, Pramod Shivaji Kumbhar, Omar Awile, Alessandro Cattabiani, Christos Kotsalos, Tristan Mathieu Carel, Samuel Marie A Melchior, Baudouin Paul Michel Maria Joseph Del Marmol, Giacomo Castiglioni, Nicola Cantarutti

Recent advances in computational neuroscience have demonstrated the usefulness and importance of stochastic, spatial reaction-diffusion simulations. However, ever increasing model complexity renders traditional serial solvers, as well as naive parallel imp ...

FRONTIERS MEDIA SA2022

Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

Francesco Spadaro

We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the deterministic on ...

AMER INST MATHEMATICAL SCIENCES-AIMS2021

Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity

Nicolas Henri Bernard Flammarion, Scott William Pesme, Loucas Pillaud-Vivien

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear networks through i ...

2021

Feedback Control Design Maximizing the Region of Attraction of Stochastic Systems Using Polynomial Chaos Expansion

Petr Listov

A feedback control design is proposed for stochastic systems with finite second moment which aims at maximising the region of attraction of the equilibrium point. Polynomial Chaos (PC) expansions are employed to represent the stochastic closed loop system ...

ELSEVIER2020

The Error-Feedback Framework: Better Rates for SGD with Delayed Gradients and Compressed Updates

Sebastian Urban Stich, Sai Praneeth Reddy Karimireddy

We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two terms: (i) a stocha ...

Microtome Publishing2020

Numerical methods for deterministic and stochastic differential equations with multiple scales and high contrasts

Giacomo Rosilho De Souza

Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...

EPFL2020

Development and verification of a methodology for neutron noise response to fuel assembly vibrations

Andreas Pautz, Hakim Ferroukhi, Abdelhamid Dokhane, Gaëtan Girardin, Dionysios Chionis

Nuclear reactors are stochastic systems, in which several parameters fluctuate even during steady-state conditions. In addition, structural components like fuel assemblies, vibrate due to strong hydraulic forces. This stochasticity is the cause of the neut ...

PERGAMON-ELSEVIER SCIENCE LTD2020

A Stochastic Conditioning Scheme for Diverse Human Motion Prediction

Mathieu Salzmann

Human motion prediction, the task of predicting future 3D human poses given a sequence of observed ones, has been mostly treated as a deterministic problem. However, human motion is a stochastic process: Given an observed sequence of poses, multiple future ...

IEEE2020

Path properties of the solution to the stochastic heat equation with Levy noise

Robert Dalang, Carsten Hao Ye Chong, Thomas Marie Jean-Baptiste Humeau

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

SPRINGER2019

The sources of sovereign risk: a calibration based on Levy stochastic processes

Sylvain Jean Pascal Carré

Governments choose to issue risky or riskless debt depending on the nature of the stochastic process of output. We use Brownian motion and Poisson shocks a modeling method in the literature on corporate default known as Levy processes to approximate a deco ...

ELSEVIER SCIENCE BV2019

Procrustes Metrics and Optimal Transport for Covariance Operators

Valentina Masarotto

Covariance operators play a fundamental role in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in con ...

EPFL2019