Almost sure approximation of unbounded operators in
The possibilities of almost sure approximation of unbounded operators in by multiples of projections or unitary operators are examined.
Almost sure asymptotic behaviour of the -neighbourhood surface area of Brownian paths
We show that whenever the -dimensional Minkowski content of a subset exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in , .
Almost sure central limit theorem for a nonstationary Gaussian sequence.
Almost sure central limit theorem for product of partial sums of strongly mixing random variables.
Almost sure central limit theorem without logarithmic sums.
Almost sure central limit theorems for strongly mixing and associated random variables.
Almost sure convergence for the maximum and the sum of nonstationary Gaussian sequences. (Almost sure convergence for the maximum and the sum of nonstationary guassian sequences.)
Almost sure exponential stability of delayed cellular neural networks.
Almost sure exponential stability of neutral differential difference equations with damped stochastic perturbations.
Almost sure finiteness for the total occupation time of an -superprocess.
Almost sure functional central limit theorem for ballistic random walk in random environment
We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
Almost sure functional limit theorem for the product of partial sums
We prove an almost sure functional limit theorem for the product of partial sums of i.i.d. positive random variables with finite second moment.
Almost sure functional limit theorems in .
Almost sure limit theorems for dependent random variables
For a sequence of dependent random variables we consider a large class of summability methods defined by R. Jajte in [jaj] as follows: For a pair of real-valued nonnegative functions g,h: ℝ⁺ → ℝ⁺ we define a sequence of “weighted averages” , where g and h satisfy some mild conditions. We investigate the almost sure behavior of such transformations. We also take a close look at the connection between the method of summation (that is the pair of functions (g,h)) and the coefficients that measure...
Almost sure path properties of branching diffusion processes
Almost sure properties of controlled diffusions and worst case properties of deterministic systems
We compare a general controlled diffusion process with a deterministic system where a second controller drives the disturbance against the first controller. We show that the two models are equivalent with respect to two properties: the viability (or controlled invariance, or weak invariance) of closed smooth sets, and the existence of a smooth control Lyapunov function ensuring the stabilizability of the system at an equilibrium.
Almost Sure Sampling Reconstruction Of Non-Band-Limited Homogeneous Random Fields
Almost sure stability of linear Itô-Volterra equations with damped stochastic perturbations.
Almost sure subexponential decay rates of scalar Itô-Volterra equations.
Almost surely limit theorems for stochastic differential equations