Free uniform measures on subinversion-closed spaces
A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process on , where is the two-dimensional torus. Here is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance. is an additive functional of , defined as , where for small . We prove that the rescaled process converges in distribution to a two-dimensional Brownian motion. As a consequence, the appropriately...
Fine regularity of stochastic processes is usually measured in a local way by local Hölder exponents and in a global way by fractal dimensions. In the case of multiparameter Gaussian random fields, Adler proved that these two concepts are connected under the assumption of increment stationarity property. The aim of this paper is to consider the case of Gaussian fields without any stationarity condition. More precisely, we prove that almost surely the Hausdorff dimensions of the range and the graph...
The subject of the paper is reciprocal influence of pure mathematics and applied sciences. We illustrate the idea by giving a review of mathematical results obtained recently, related to the model of stochastic gene expression due to Lipniacki et al. [38]. In this model, featuring mRNA and protein levels, and gene activity, the stochastic part of processes involved in gene expression is distinguished from the part that seems to be mostly deterministic, and the dynamics is expressed by means of a...
We analyse the case of certificates of environmental improvements and full cooperation of two identical agents. We model pollution levels as geometric Brownian motions with quadratic costs of improvements. Our main result is the construction of the optimal improvements strategy in the case of separate actions, collusive actions and fusion. In certain range of the model parameters, the fusion solution generates lower pollution levels than separate and collusive actions.
We consider an initial and Dirichlet boundary value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. Discretizing the space-time white noise a modelling error is introduced and a regularized fourth-order linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the regularized problem are constructed by using, for discretization in space, a Galerkin finite element method...