In [1] Diffusion algebras have been introduced in the context of onedimensional stochastic processes with exclusion in statistical mechanics. While this reference is focused on the needs of the physicist reader and thus states results without proofs and focuses on the discussion of lower-dimensional examples, it is the purpose of this paper to present a construction formalism for Diffusion alge...

It is shown that the physical mechanism of thermally activated subcritical crack growth is always a stochastic process and leads, therefore, to probabilistic crack propagation. This process is the result of the random breaking of atomic bonds and has to be clearly distinguished f rom the well known Weibull distribution. A Markov chain analysis leads to the normal distribution of crack sizes. Th...

This paper provides a new version of the condition of Di Nunno et al. (2003), Ankirchner and Imkeller (2005) and Biagini and Øksendal (2005) ensuring the semimartingale property for a large class of continuous stochastic processes. Unlike our predecessors, we base our modeling framework on the concept of portfolio proportions which yields a short self-contained proof of the main theorem, as wel...

In this paper it is shown that one can estimate the sum of the weights used to form a stationary moving average stochastic process based on nonnegative random variables by taking the limit in probability of suitable quotients, even when the random variables involved have infinite expectation.

We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability density functions of these random variables have very different scalings in time. We analyze successively the cases where this distribution is narrow, where ...

The mechanics of transport and ow in a random porous medium are addressed in this paper. The hydraulic properties of the porous medium are modeled as spatial random processes. The heterogeneity of the medium is modeled as a superposition of scales of heterogeneity that are statistically uncorrelated. The stochastic process making up a hydraulic property is thus represented as a linear combinati...