Stationary random graphs on with prescribed iid degrees and finite mean connections.
Stationary random graphs with prescribed iid degrees on a spatial Poisson process.
Stationary solutions and forward equations for controlled and singular martingale problems.
Stationary solutions for integer-valued autoregressive processes.
Statistical causality and adapted distribution
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 conditions for two stochastic processes to have the same adapted distribution. For this purpose we use the concept...
Statistical convergence of a sequence of random variables and limit theorems
In this paper the ideas of three types of statistical convergence of a sequence of random variables, namely, statistical convergence in probability, statistical convergence in mean of order and statistical convergence in distribution are introduced and the interrelation among them is investigated. Also their certain basic properties are studied.
Statistical Inference about the Drift Parameter in Stochastic Processes
In statistical inference on the drift parameter in the Wiener process with a constant drift there is a large number of options how to do it. We may, for example, base this inference on the properties of the standard normal distribution applied to the differences between the observed values of the process at discrete times. Although such methods are very simple, it turns out that more appropriate is to use the sequential methods. For the hypotheses testing about the drift parameter it is more...
Statistical inference for stochastic parabolic equations: a spectral approach.
Statistical problems on point processes
Statistical procedures for spatial point pattern recognition.
Spatial structures in the form of point patterns arise in many different contexts, and in most of them the key goal concerns the detection and recognition of the underlying spatial pattern. Particularly interesting is the case of pattern analysis with replicated data in two or more experimental groups. This paper compares design-based and model-based approaches to the analysis of this kind of spatial data. Basic questions about pattern detection concern estimating the properties of the underlying...
Statistical properties of long return times in type I intermittency.
Stein estimation for infinitely divisible laws
Unbiased risk estimation, à la Stein, is studied for infinitely divisible laws with finite second moment.
Stereology of extremes; size of spheroids
The prediction of size extremes in Wicksell’s corpuscle problem with oblate spheroids is considered. Three-dimensional particles are represented by their planar sections (profiles) and the problem is to predict their extremal size under the assumption of a constant shape factor. The stability of the domain of attraction of the size extremes is proved under the tail equivalence condition. A simple procedure is proposed of evaluating the normalizing constants from the tail behaviour of appropriate...
Stochastic affine evolution equations with multiplicative fractional noise
A stochastic affine evolution equation with bilinear noise term is studied, where the driving process is a real-valued fractional Brownian motion with Hurst parameter greater than . Stochastic integration is understood in the Skorokhod sense. The existence and uniqueness of weak solution is proved and some results on the large time dynamics are obtained.
Stochastic analysis and local times for (N, d)-Wiener process
Stochastic analysis of Bernoulli processes.
Stochastic antiderivational equations on non-Archimedean Banach spaces.
Stochastic approximations of the solution of a full Boltzmann equation with small initial data
Stochastic approximations of the solution of a full Boltzmann equation with small initial data
This paper gives an approximation of the solution of the Boltzmann equation by stochastic interacting particle systems in a case of cut-off collision operator and small initial data. In this case, following the ideas of Mischler and Perthame, we prove the existence and uniqueness of the solution of this equation and also the existence and uniqueness of the solution of the associated nonlinear martingale problem. Then, we first delocalize the interaction by considering a mollified Boltzmann...
Stochastic bilinear equations with fractional Gaussian noise in Hilbert space