
Stable approximation schemes for optimal filters
We explore a general truncation scheme for the approximation of (possibl...
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Estimating the logarithm of characteristic function and stability parameter for symmetric stable laws
Let X_1,…,X_n be an i.i.d. sample from symmetric stable distribution wit...
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A modification of quasiNewton's methods helping to avoid saddle points
We recall that if A is an invertible and symmetric real m× m matrix, the...
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Palindromic Length and Reduction of Powers
Given a nonempty finite word v, let PL(v) be the palindromic length of v...
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Pebble Exchange Group of Graphs
A graph puzzle Puz(G) of a graph G is defined as follows. A configurati...
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Shadowing for families of endomorphisms of generalized group shifts
Let G be a countable monoid and let A be an Artinian group (resp. an Art...
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A squarefree term not occurring in the Leech sequence
Let < a r r a y > The Leech sequence L is the squarefree sequence ...
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Stability of trigonometric approximation in L^p and applications to prediction theory
Let Γ be an LCA group and (μ_n) be a sequence of bounded regular Borel measures on Γ tending to a measure μ_0. Let G be the dual group of Γ, S be a nonempty subset of G ∖{ 0 }, and [𝒯(S)]_μ_n,p the subspace of L^p(μ_n), p ∈ (0,∞), spanned by the characters of Γ which are generated by the elements of S. The limit behaviour of the sequence of metric projections of the function 1 onto [𝒯(S)]_μ_n,p as well as of the sequence of the corresponding approximation errors are studied. The results are applied to obtain stability theorems for prediction of weakly stationary or harmonizable symmetric pstable stochastic processes. Along with the general problem the particular cases of linear interpolation or extrapolation as well as of a finite or periodic observation set are studied in detail and compared to each other.
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