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Currently displaying 1 – 3 of 3

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Hölder versions of Banach space valued random fields.

Račkauskas, Alfredas; Suquet, Charles — 2001

Georgian Mathematical Journal

Hölderian invariance principle for Hilbertian linear processes

Alfredas Račkauskas; Charles Suquet — 2009

ESAIM: Probability and Statistics

Let ${(ξ_{n})}_{n \geq 1}$ be the polygonal partial sums processes built on the linear processes $X_{n} = \sum_{i \geq 0} a_{i} (ϵ_{n - i})$ , ≥ 1, where ${(ϵ_{i})}_{i \in ℤ}$ are i.i.d., centered random elements in some separable Hilbert space $ℍ$ and the 's are bounded linear operators $ℍ \to ℍ$ , with $\sum_{i \geq 0} ∥ a_{i} ∥ < \infty$ . We investigate functional central limit theorem for $ξ_{n}$ in the Hölder spaces $H_{ρ}^{o} (ℍ)$ of functions $x : [0, 1] \to ℍ$ such that || uniformly in , where , 0 ≤ ≤ 1 with 0 ≤ ≤ 1/2 and slowly varying at infinity. We obtain the $H_{ρ}^{o} (ℍ)$ weak convergence of $ξ_{n}$ to some $ℍ$ valued Brownian motion...

Security price modelling by a binomial tree

Remigijus Leipus; Alfredas Račkauskas — 1999

Applicationes Mathematicae

We consider multidimensional tree-based models of arbitrage-free and path-independent security markets. We assume that no riskless investment exists. Contingent claims pricing and hedging problems in such a market are studied.

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