[en] Stochastic processes are widely used in plasma physics and have provided very useful tools to describe the behavior of this disordered medium. The resulting physical effects have received considerable attention and it has motivated the edition of this book, following a workshop on the same subject, held at the 'Institut d'Etudes Scientifiques de Cargese' (Corsica, France) in 1979. The book contains thirty contributed and review papers

No abstract available

[en] Given a classical stationary stochastic process, a corresponding quantum stochastic process is constructed. As an example, the Ornstein-Uhlenbeck process is used to construct the quantum process whose existence was suggested by the work of Ford, Kac and Mazur

[en] The purpose of this paper is twofold. First, we introduce the general formalism of evolutionary genetics dynamics involving fitnesses, under both the deterministic and stochastic setups, and chiefly in discrete time. In the process, we particularize it to a one-parameter model where only a selection parameter is unknown. Then and in a parallel manner, we discuss the problems of estimation of the selection parameter on the basis of a single-generation frequency distribution shift under both deterministic and stochastic evolutionary dynamics. In the stochastics, we consider both the celebrated Wright–Fisher and Moran models

[en] A number of problems, including the calculation of magnetic field line trajectories in three-dimensional systems, can be treated as a mapping of a plane onto itself. KAM theory has shown that these trajectories can be either periodic, restricted to a KAM curve, or ergodic and thus filling a finite fraction of the available phase space. The problem addressed here is finding when particular KAM surfaces exist. The method adopted is to study numerically the periodic orbits of a particular mapping. The guiding hypothesis is that the disappearance of a KAM surface is associated with a sudden change from stability to instability of all nearby periodic orbits

No abstract available

[en] For the residues of the division of the n members of an arithmetical progression by a real number N is proved the tending to 0 of the Kolmogorov's stochasticity parameter λ_n, when n tends to infinity, providing that the progression step is commensurable with N. On the contrary, when the step is incommensurable with N, the paper describes some examples, where the stochasticity parameter λ_n does not tend to zero, and even attains (infrequently) some arbitrary large values. Both the too small and the too large values of the stochasticity parameter show the small probability of the randomness of the sequence, for which they have been counted. Thus, the long arithmetical progressions' stochasticity degree is much smaller than that of the geometrical progressions (which provide temperate values of the stochasticity parameter, similarly to its value for the genuinely random sequences). (author)

[en] An experiment on the transition to turbulence in a plasma with a limited number of discrete modes of the collisionless drift instability is analysed in terms of the present-day picture of intrinsic stochasticity. The modes are described as an ensemble of weakly coupled van der Pol oscillators which are initially synchronized but lose synchronization because of finite Larmor radius effects and length effects, which cause detuning

[en] In this paper, we introduce stochastic g-fractional integrals of order $\mathrm{\alpha <!--\; ??\; -->}$, containing stochastic fractional integrals (Hafiz in Stoch Anal Appl 22:507–523, 2004), stochastic integral (Shaked and Shanthikumar in Adv Appl Prob 20:427–446, 1988) and stochastic pseudo integrals (Agahi in Stat Probab Lett 124:41–48, 2017). We determine the upper and lower bounds of stochastic g-fractional integrals for convex stochastic processes, generalizing some previous results in Kotrys (Aequat Math 83:143–151, 2012), Agahi (Aequat Math 90:765–772, 2016; 2017) and Agahi and Babakhani (Aequat Math 90:1035–1043, 2016).

[en] A fast gradient method requiring only one projection is proposed for smooth convex optimization problems. The method has a visual geometric interpretation, so it is called the method of similar triangles (MST). Composite, adaptive, and universal versions of MST are suggested. Based on MST, a universal method is proposed for the first time for strongly convex problems (this method is continuous with respect to the strong convexity parameter of the smooth part of the functional). It is shown how the universal version of MST can be applied to stochastic optimization problems.