In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian elds. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution.

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize previous works by Nourdin and Nualart [J. Theoret. Probab. 23 (2010) 39–64] and Harnett and Nualart [Stochastic Process. Appl. 122 (2012) 3460–3505], and pr...

The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (m, n)-hyperring R such that the quotient space is an (m, n)-ring, to introdu...

L et us apply our newly acquired tools to the fundamental diagnostics in dynamics: Is a given system ‘chaotic’? And if so, how chaotic? If all points in example 2.3 a neighborhood of a trajectory converge toward the same orbit, the attractor is a fixed point or a limit cycle. However, if the attractor is strange, any two section 1.3.1 trajectories x(t) = f (x0) and x(t)+δx(t) = f (x0 + δx0) tha...

Within a simple quantization scheme, observables for a large class of finite dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. This procedure is shown to produce a complete set of densely defined operators on a physical Hilbert space for which an inner product is identified and to provide reasonable results for simple test c...

A method is given for a study of a nonlinear evolution equation for finding “slow” invariant manifolds. The method is studied for the evolution problem u̇=−Au + Au ,u / u ,u u, u 0 =u0, where A is a linear, self-adjoint, possibly unbounded operator in a Hilbert space. Global existence and uniqueness of the solution to this problem are proven. Asymptotic behavior of the solution as t→ is studied....

Let X be a compact Hausdorff space. We study finite-to-one map-pings r : X → X, onto X, and measures on the corresponding projective limit space X∞(r). We show that the invariant measures on X∞(r) correspond in a one-to-one fashion to measures on X which satisfy two identities. Moreover, we identify those special measures on X∞(r) which are associated via our correspondence with a function V on...

We show that the classical Szasz analytic function SN (f)(x) is related to the Bergman kernel for the Bargmann-Fock space. Then we generalize this relation to any noncompact toric Kähler manifold, defining the generalized Szasz analytic function ShN (f)(x). Then we will prove the complete asymptotic expansion of ShN (f)(x) and its scaling limit property. As examples, we will compute the general...

The method of periodic projections consists in iterating projections onto m closed convex subsets of a Hilbert space according to a periodic sweeping strategy. In the presence ofm ≥ 3 sets, a long-standing question going back to the 1960s is whether the limit cycles obtained by such a process can be characterized as the minimizers of a certain functional. In this paper we answer this question i...

Global dynamical behaviors of the competitive Lotka-Volterra system even in 3-dimension are not fully understood. The Lyapunov function can provide us such knowledge once it is constructed. In this paper, we construct explicitly the Lyapunov function in three examples of the competitive LotkaVolterra system for the whole state space: (1) the general 2-dimensional case; (2) a 3-dimensional model...