The microscopic details of printing often are unnoticed by humans, but can make differences that affect machine recognition of printed text. Models of the defects introduced into images by printing can be used to improve machine recognition. A probabilistic model used to generate images showing toner placement bears similarities to actual printed images. An equation derived for the average cove...

The Persistent Turning Walker Model (PTWM) was introduced by Gautrais et al in Mathematical Biology for the modelling of fish motion. It involves a nonlinear pathwise functional of a non-elliptic hypo-elliptic diffusion. This diffusion solves a kinetic Fokker-Planck equation based on an Ornstein-Uhlenbeck Gaussian process. The long time “diffusive” behavior of this model was recently studied by...

This paper is about parameter estimation for models described by a continuoustime state equation from discrete-time measurements. Guaranteed solutions to this problem are proposed in probabilistic and bounded-error contexts, based on Müller’s theorems and interval analysis. In a probabilistic context where parameter estimation boils down to parameter optimization, this makes it possible to char...

The possibility of using non-deterministic circuit components has been gaining significant attention in recent years. modeling and simulation their circuits require novel approaches, as now the state a at an arbitrary moment time cannot be precisely predicted. Generally, these should described terms probabilities, variables calculated on average, correlation functions used to explore interrelat...

We study the three-dimensional cubic nonlinear wave equation (NLW) with random initial data below L 2 (

We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid–structure interaction between 3D incompressible, Stokes flow and elastodynamics of stretched membrane. The focus is on (rough) data, often arising in real-life problems, which it known that the deterministic problem ill-posed. show random perturbations such data give rise almost surely to existence uni...

In this paper we will give a probabilistic representation for the heat flow of harmonic map with time-dependent Riemannian metric via forward–backward stochastic differential equation on manifolds. Moreover, can provide an alternative method proof existence unique local solution metric.

It is known that a stochastic differential equation (SDE) induces two probabilistic objects, namely a difusion process and a stochastic flow. While the diffusion process is determined by the innitesimal mean and variance given by the coefficients of the SDE, this is not the case for the stochastic flow induced by the SDE. In order to characterize the stochastic flow uniquely the innitesimal cov...