We give a direct proof of the Harnack inequality for a class of Kolmogorov operators associated with a linear SDE and we find the explicit expression of the optimal Harnack constant. We discuss some possible implication of the Harnack inequality in finance: specifically we infer no-arbitrage...

In this work, the process of distribution functions of a one-dimensional super-Lévy process with general branching mechanism is characterized as the pathwise unique solution of a stochastic integral equation driven by time–space Gaussian white noises and Poisson random measures. This...

The objective of the paper is to identify and investigate all possible types of asymptotic behavior for the maximum likelihood estimators of the unknown parameters in the second-order linear stochastic ordinary differential equation driven by Gaussian white noise. The emphasis is on the...

In the present study, the buffering effect of magnetite nanoparticles (Fe3O4) dispersed in an aqueous solution on the local pH value is investigated. It manifests itself in the fact that when some amount of acid or base is added to the solution then the solution near the nanoparticles surface...

Under the assumption that the infinite product of the evolution process converges almost surely, the set of strong solutions is characterized by a compact space T, which may be regarded as the set of possible initial states. More precisely, any strong solution may be represented as the result of...

A stochastic heat equation on an unbounded nested fractal driven by a general stochastic measure is investigated. Existence, uniqueness and continuity of the mild solution are proved provided that the spectral dimension of the fractal is less than 4/3.

Simulation estimators, such as indirect inference or simulated maximum likelihood, are successfully employed for estimating stochastic differential equations. They adjust for the bias (inconsistency) caused by discretization of the underlying stochastic process, which is in continuous time. The...

By using an exact functional formalism we characterize general stationary properties of linear memory-like Langevin equations, including the case of delay equations driven by arbitrary noises. Spectral properties and stationary distributions are analyzed in detail.

The concentration of a tracer injected into a packed bed is studied as a function of the time and of the axial position in the frame-work of a phenomenological model of irregular packed bed. For that we consider a one-dimensional Fick diffusion equation with a stochastic porosity. To perform an...