Related papers: Fractional Stochastic Loewner Evolution and Scalin…
While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…
Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…
This paper studies high-dimensional curve time series with common stochastic trends. A dual functional factor model structure is adopted with a high-dimensional factor model for the observed curve time series and a low-dimensional factor…
The (chordal) Loewner differential equation encodes certain curves in the half-plane (aka traces) by continuous real-valued driving functions. Not all curves are traces; the latter can be defined via a geometric condition called the local…
This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them.…
Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…
Growth fronts of slime molds are characterized through a direct geometric analysis based on Loewner evolutions, using experimentally acquired time-resolved images. The associated Loewner driving functions reconstructed from expanding…
The aim of these notes is threefold. First, we discuss geometrical aspects of conformal covariance in stochastic Schramm-Loewner evolutions (SLEs). This leads us to introduce new ``dipolar'' SLEs, besides the known chordal, radial or…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
Fractal dimension is an effective scaling exponent of characterizing scale-free phenomena such as cities. Urban growth can be described with time series of fractal dimension of urban form. However, how to explain the factors behind fractal…
We obtain a first order differential equation for the driving function of the chordal Loewner differential equation in the case where the domain is slit by a curve which is a trajectory arc of certain quadratic differentials. In particular…
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. Despite the existence of…
A Fokker Planck equation on fractal curves is obtained, starting from Chapmann-Kolmogorov equation on fractal curves. This is done using the recently developed calculus on fractals, which allows one to write differential equations on…
Levy flights and fractional Brownian motion (fBm) have become exemplars of the heavy tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm)…
A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…
In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…
We analyse a random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, hence plays an…