Fredholm determinants
The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.
From a kinetic equation to a diffusion under an anomalous scaling
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...
From an example of Lévy's
From convergence of operator semigroups to gene expression, and back again
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...
From Tanaka's formula to Ito's formula : distributions, tensor products and local times
Frontière de Martin du dual de SU(2)
Fubini's theorem for double Wiener integrals and the variance of the brownian path
Function decompositions related to the Luzin N-property.
Function spaces related to continuous negative definite functions: ψ-Bessel potential spaces [Book]
Functional integral representations for self-avoiding walk.
Functionals associated with self-intersections of the planar brownian motion
Funktionen homogener Markoffscher Ketten als homogene bzw. inhomogene Markoffsche Ketten
Further exponential generalization of Pitman's theorem.
Further probabilistic analysis of the Fisher–Kolmogorov–Petrovskii–Piscounov equation : one sided travelling-waves
Further pseudodifferential operators generating Feller semigroups and Dirichlet forms.
We prove for a large class of symmetric pseudo differential operators that they generate a Feller semigroup and therefore a Dirichlet form. Our construction uses the Yoshida-Hille-Ray Theorem and a priori estimates in anisotropic Sobolev spaces. Using these a priori estimates it is possible to obtain further information about the stochastic process associated with the Dirichlet form under consideration.
Fuzzy Markov chains: uncertain probabilities.
We consider finite Markov chains where there are uncertainties in some of the transition probabilities. These uncertainties are modeled by fuzzy numbers. Using a restricted fuzzy matrix multiplication we investigate the properties of regular, and absorbing, fuzzy Markov chains and show that the basic properties of these classical Markov chains generalize to fuzzy Markov chains.