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Displaying similar documents to “On the extremal behavior of sub-sampled solutions of stochastic difference equations.”

Limit theorems for number of diffusion processes, which did not absorb by boundaries

Aniello Fedullo, Vitalii Gasanenko (2006)

Open Mathematics

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We have random number of independent diffusion processes with absorption on boundaries in some region at initial time t = 0. The initial numbers and positions of processes in region is defined by the Poisson random measure. It is required to estimate the number of the unabsorbed processes for the fixed time τ > 0. The Poisson random measure depends on τ and τ → ∞.

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...

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...