Related papers: A density property for stochastic processes
In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of…
We discuss the relationship between discrete-time processes (chains) and one-dimensional Gibbs measures. We consider finite-alphabet (finite-spin) systems, possibly with a grammar (exclusion rule). We establish conditions for a stochastic…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
We study the limiting degree distribution of the vertex splitting model introduced in \cite{DDJS:2009}. This is a model of randomly growing ordered trees, where in each time step the tree is separated into two components by splitting a…
We investigate a class of stochastic aggregation processes involving two types of clusters: active and passive. The mass distribution is obtained analytically for several aggregation rates. When the aggregation rate is constant, we find…
For a given quasi-regular positivity preserving coercive form, we construct a family of ($\sigma$-finite) distribution flows associated with the semigroup of the form. The canonical cadlag process equipped with the distribution flows…
Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…
In this paper we study some basic properties of strong {\lambda}- statistical convergence of sequences in probabilistic metric (PM) spaces. We also introduce and study the notion of strong {\lambda}-statistically Cauchyness. Further…
We investigate a class of reaction processes in which particles move ballistically and react upon colliding. We show that correlations between velocities of colliding particles play a crucial role in the long time behavior. In the…
Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods…
Two transformations $\mathcal{A}_1$ and $\mathcal{A}_2$ of L\'{e}vy measures on $\mathbb{R}^d$ based on the arcsine density are studied and their relation to general Upsilon transformations is considered. The domains of definition of…
It is revealed that distribution functions of practical gases relate to singularities and such singularities can, with molecular motion, spread to the entire region of interest. It is also shown that even common continuous distribution…
The density of a rational language can be understood as the frequency of some "pattern" in the shift space, for example a pattern like "words with an even number of a given letter." We study the density of group languages, i.e. rational…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
We consider a class of stochastic kinetic equations, depending on two time scale separation parameters $\epsilon$ and $\delta$: the evolution equation contains singular terms with respect to $\epsilon$, and is driven by a fast ergodic…
Assume that a family of stochastic processes on some Polish space $E$ converges to a deterministic process; the convergence is in distribution (hence in probability) at every fixed point in time. This assumption holds for a large family of…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…
We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…
We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic processes arising from a dynamical system, by evaluating a given…