Stationary processes are stochastic processes whose probabilistic structure is unaffected by shifts in time. According to the interpretation of the term “probabilistic structure”, one distinguishes weak sense stationary processes, where only the covariance structure is supposed to be invariant, and strict sense stationary processes, for which all finitedimensional distributions have to remain t...

The aim of this work is to provide an introduction into the theory of infinite dimensional stochastic processes. The thesis contains the paper A class of infinite dimensional stochastic processes with unbounded diffusion written at Linköping University during 2012. The aim of that paper is to take results from the finite dimensional theory into the infinite dimensional case. This is done via th...

With this paper I start the investigation of the following claim: logic (and mathematics) is reliable because it is rooted on the laws of chance. To show this I introduce a stochastic semantics for logic where propositions are interpreted into sets of observables (i.e. sets of trajectories of suitable stochastic processes) whose elements describe some symmetries of chance. A validity theorem is...

A fundamental problem in statistics is to develop models based on a sample of observations and drawing inferences using the model so developed. In growth modeling, data are usually collected over time. One characteristic of such data is that the successive observations are dependent. Each observation of the observed data series Yt may be considered as a realization of a stochastic process {Yt},...

We are going to give necessary and suucient conditions for a multivariate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes .

At any point in time, a cleared parcel of forest land (CPFL) used for swidden agriculture exists in either the fallow or in the non-fallow state. Further, the practice of swidden agriculture requires one to operate in an environment of uncertainty. These two points notwithstanding, there are virtually no probabilistic models of swidden agriculture that explicitly account for the above dichotomy...

In the paper D.Hoover, J. Keisler : Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is hard to prove directly, so we continue the work of Keisler and Hoover in finding sufficient conditi...

Discussion on the limits in distribution of processes Y under joint rescaling of space and time is presented in this paper. The results due to Lamperti (1962), Weissman (1975), Hudson & Mason (1982) and Laha & Rohatgi (1982) are improved here.

Temporal variation in the composition of species assemblages could be the result of deterministic processes driven by environmental change and/or stochastic processes of colonization and local extinction. Here, we analyzed the relative roles of deterministic and stochastic processes on bird assemblages in an agricultural landscape of southwestern France. We first assessed the impact of land cov...