Displaying similar documents to “Weak convergence of summation processes in Besov spaces”

Functional central limit theorems for seeds in a linear birth and growth model

A. Dziwisz, W. Szczotka (2016)

Applicationes Mathematicae

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A problem of heredity of mixing properties (α-mixing, β-mixing and ρ-mixing) from a stationary point process on ℝ × ℝ₊ to a sequence of some of its points called 'seeds' is considered. Next, using the mixing properties, several versions of functional central limit theorems for the distances between seeds and the process of the number of seeds are obtained.

Relationship between Extremal and Sum Processes Generated by the same Point Process

Pancheva, E., Mitov, I., Volkovich, Z. (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17. We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^d as well as for the associated with it sum and extremal processes on an open subset S . The complement of S turns out to be the explosion area of the limit Poisson point process. In order to prove our criterion for weak convergence of the sum processes we introduce and study sum processes...

Weak Hölder convergence of processes with application to the perturbed empirical process

Djamel Hamadouche, Charles Suquet (1999)

Applicationes Mathematicae

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We consider stochastic processes as random elements in some spaces of Hölder functions vanishing at infinity. The corresponding scale of spaces C 0 α , 0 is shown to be isomorphic to some scale of Banach sequence spaces. This enables us to obtain some tightness criterion in these spaces. As an application, we prove the weak Hölder convergence of the convolution-smoothed empirical process of an i.i.d. sample ( X 1 , . . . , X n ) under a natural assumption about the regularity of the marginal distribution function...

Renormalization group of and convergence to the LISDLG process

Endre Iglói (2004)

ESAIM: Probability and Statistics

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The LISDLG process denoted by J ( t ) is defined in Iglói and Terdik [ESAIM: PS 7 (2003) 23–86] by a functional limit theorem as the limit of ISDLG processes. This paper gives a more general limit representation of J ( t ) . It is shown that process J ( t ) has its own renormalization group and that J ( t ) can be represented as the limit process of the renormalization operator flow applied to the elements of some set of stochastic processes. The latter set consists of IGSDLG processes which are generalizations...

Process-level large deviations for nonlinear Hawkes point processes

Lingjiong Zhu (2014)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.