The thesis is devoted to the study of solutions to the following linear recursion: Xn+1 = γXn + ξn, where γ ∈ (0, 1) is a constant and (ξn)n∈Z is a stationary and ergodic sequence of normal variables with random means and variances. More precisely, we assume that ξn = μn + σnεn, where (ε)n∈Z is an i.i.d. sequence of standard normal variables and (μn, σn)n∈Z is a stationary and ergodic process i...

When an observer moves through an environment containing stationary and moving objects, he or she must be able to determine which objects are moving relative to the others in order to navigate successfully and avoid collisions. We investigated whether image speed can be used as a cue to detect a moving object in the scene. Our results show that image speed can be used to detect moving objects a...

The rate of cooling (heating) experimental liquids is investigated separately for five thermocouples located at different heights the probe. Research carried out on an stand in system "environment I — body II", where I" water, and "body II" liquid medium a thin metal cylindrical shell under conditions free convection. studied test liquids: sunflower oil, distilled glycerin. analysis processes d...

Estimation theory in a nonstationary environment has been very popular in recent years. Existing studies focus on nonstationarity in parametric linear, parametric nonlinear and nonparametric nonlinear models. In this paper, we consider a partially linear model of the form Yt = Xτ t α+g(Vt)+ t, t = 1, · · · , n, where {Vt} is a sequence of β–null recurrent Markov chains, {Xt} is a sequence of ei...

Bayesian geostatistical models applied to malaria risk data quantify the environment-disease relations, identify significant environmental predictors of malaria transmission and provide model-based predictions of malaria risk together with their precision. These models are often based on the stationarity assumption which implies that spatial correlation is a function of distance between locatio...

While adaptive filtering is in principle intended for tracking non-stationary systems, most adaptive filtering algorithms have been designed for converging to a fixed unknown filter. When actually confronted with a non-stationary environment, they possess just one parameter (stepsize, forgetting factor) to adjust their tracking capability. Virtually the only existing optimal approach is the Kal...

We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The environment is supposed to be stationary and ergodic. For A ⊂ R , let Zn(A) be the number of particles of generation n located in A. We show central l...

This study aims at improving the understanding of mechanisms responsible for cell sensitivity to extracellular environment. We explain how substrate mechanical properties can modulate the force regulation of cell sensitive elements primarily adhesion sites. We present a theoretical and experimental comparison between two radically different approaches of the force regulation of adhesion sites t...