相关论文: On superstatistical multiplicative-noise processes
Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…
This paper addresses the challenge of a particular class of noisy state observations in Markov Decision Processes (MDPs), a common issue in various real-world applications. We focus on modeling this uncertainty through a confusion matrix…
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…
This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing…
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 study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
Recent experiments have shown that stochastic effects exerted at the level of translation contribute a substantial portion of the variation in abundance of proteins expressed at moderate to high levels. This study analyzes translational…
We prove existence and asymptotic behavior of the transition density for a large class of subordinators whose Laplace exponents satisfy lower scaling condition at infinity. Furthermore, we present lower and upper bounds for the density.…
The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the…
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…
Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…
We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a Time-Dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled…
The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is…
We propose a new approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations. Our formalism is based on a nonextensive generalization of the Wiener process. This allow us to obtain, in addition…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are found which…
This paper studies the behavior of solitons in the Korteweg-de Vries equation under the influence of multiplicative noise. We introduce stochastic processes that track the amplitude and position of solitons based on a rescaled frame…
We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients,…
A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are…
A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the…