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On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

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Stochastic particle transport by deep-water irregular breaking waves

Debbie Eeltink

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

Cambridge2023

Nonparametric 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 ...

Amsterdam2023

THE COMPACT SUPPORT PROPERTY FOR SOLUTIONS TO THE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH COLORED NOISE

Jaeyun Yi

We study the compact support property for solutions of the following stochastic partial differential equations: partial derivative tu=aijuxixj(t,x)+biuxi(t,x)+cu+h(t,x,u(t,x))F-center dot(t,x),(t,x)is an element of(0,infinity)xRd,where F-center dot is a sp ...

Philadelphia2023

Normalized Gaussian path integrals

Giulio Corazza

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...

AMER PHYSICAL SOC2020

Gaussian and sparse processes are limits of generalized Poisson processes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Generating Sparse Stochastic Processes Using Matched Splines

Michaël Unser, Leello Tadesse Dadi, Shayan Aziznejad

We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions of linear ordinary differential equations driven by Levy white noises. A recent paper showed that these processes are limits in law of generalized compound-P ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Content Based Status Updates

Emre Telatar, Elie Najm, Rajai Nasser

Consider a stream of status updates generated by a source, where each update is of one of two types: high priority or ordinary (low priority). These updates are to be transmitted through a network to a monitor. However, the transmission policy of each pack ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Calculus of variations: A differential form approach

Swarnendu Sil

We study integrals of the form integral(Omega) f(d omega(1), ..., d omega(m)), where m >= 1 is a given integer, 1

WALTER DE GRUYTER GMBH2019

Feedback and Mediation in Causal Inference Illustrated by Stochastic Process Models

Mats Julius Stensrud

The concept of causality is naturally related to processes developing over time. Central ideas of causal inference like time-dependent confounding (feedback) and mediation should be viewed as dynamic concepts. We shall study these concepts in the context o ...

2018

Content Based Status Updates

Emre Telatar, Elie Najm, Rajai Nasser

Consider a stream of status updates generated by a source, where each update is of one of two types: priority or ordinary; these updates are to be transmitted through a network to a monitor. We analyze a transmission policy that treats updates depending on ...

2018