Related papers: Shot noise multifractal model for turbulent pseudo…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and…
Multiplicative processes and multifractals have earned increased popularity in applications ranging from hydrodynamic turbulence to computer network traffic, from image processing to economics. We analyse the multifractality of the recently…
This article present a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade. One multiplicatively…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, we extend the method to the joint generation of pairs of…
This paper examines the temporal evolution of a two-stage stochastic model for spherical random fields. The model uses a time-fractional stochastic hyperbolic diffusion equation, which describes the evolution of spherical random fields on…
We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the…
The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation,…
A new discrete-time shot noise Cox process for spatiotemporal data is proposed. The random intensity is driven by a dependent sequence of latent gamma random measures. Some properties of the latent process are derived, such as an…
Multifractal formalisms provide an apt framework to study random cascades in which multifractal spectrum width $\Delta\alpha$ fluctuates depending on the number of estimable power-law relationships. Then again, multifractality without…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
This dissertation discusses the intermitency phenomenon in three models of turbulence, employing analytical and numerical techniques in the analysis of stochastic processes and the probability distributions which they induce. The initial…
Turbulence is prevalent in nature and industry, from large-scale wave dynamics to small-scale combustion nozzle sprays. In addition to the multi-scale nonlinear complexity and both randomness and coherent structures in its dynamics,…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as the energy dissipation in fully developed turbulence. We propose a dynamical generalization describing the energy…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess,…