Related papers: Diffusions of Multiplicative Cascades
Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of…
Multiplicative cascades, under weak or strong disorder, refer to sequences of positive random measures $\mu_{n,\beta}, n = 1,2,\dots$, parameterized by a positive disorder parameter $\beta$, and defined on the Borel $\sigma$-field…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
Conditions on the generator of a Markov process to control the fluctuations of its bridges are found. In particular, continuous time random walks on graphs and gradient diffusions are considered. Under these conditions, a concentration of…
This is a survey paper about reciprocal processes. The bridges of a Markov process are also Markov. But an arbitrary mixture of these bridges fails to be Markov in general. However, it still enjoys the interesting properties of a reciprocal…
Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as for example the energy dissipation field of fully developed turbulence. A dynamical generalisation of these models is…
Multiplicative random cascade model naturally reproduces the intermittency or multifractality, which is frequently shown among hierarchical complex systems such as turbulence and financial markets. As described herein, we investigate the…
Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…
Cascades on random networks are typically analyzed by assuming they map onto percolation processes and then are solved using generating function formulations. This approach assumes that the network is infinite and weakly connected, yet…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
We demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artefact of the observation procedure. Taking the latter into…
The reciprocal class of a Markov path measure is the set of all mixtures of its bridges. We give characterizations of the reciprocal class of a continuous-time Markov random walk on a graph. Our main result is in terms of some reciprocal…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a…
The invariant measure is a fundamental object in the theory of Markov processes. In finite dimensions a Markov process is defined by transition rates of the corresponding stochastic matrix. The Markov tree theorem provides an explicit…
We consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically.…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
Markovian properties of a discrete random multiplicative cascade model of log-normal type are discussed. After taking small-scale resummation and breaking of the ultrametric hierarchy into account, qualitative agreement with Kramers-Moyal…
A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…