arXiv subjects

R. Kapica

Publications and source records attributed to R. Kapica.

2 recordsLinked to original sources

arXiv2017

Random iteration with place dependent probabilities

Markov chains arising from random iteration of functions $S_θ:X\to X$, $θ\in Θ$, where $X$ is a Polish space and $Θ$ is arbitrary set of indices are considerd. At $x\in X$, $θ$ is sampled from distribution $θ_x$ on $Θ$ and $θ_x$ are different for different $x$. Exponential convergence to a unique invariant measure is proved. This result is applied to case of random affine transformations on ${\mathbb R}^d$ giving existence of exponentially attractive perpetuities with place dependent probabilities.

math.PR↗

arXiv2011

The Stability of some stochastic processes

We formulate and prove a new criterion for stability of e-processes. It says that any e-process which is averagely bounded and concentrating is asymptotically stable. In the second part, we show how this general result applies to some shell models (the Goy and the Sabra model). Indeed, we manage to prove that the processes corresponding to these models satisfy the e-process property. They are also averagely bounded and concentrating. Consequently, their stability follows.

math-ph↗