| Abstract
| - For a general càdlàg Lévy process X on a separable Banach space V we estimate values of inf c≥0 { ψ( c) + inf Y∈ A X( c) 𝔼TV( Y,[0, T])}, where AX( c) is the family of processes on V adapted to the natural filtration of X, a.s. approximating paths of X uniformly with accuracy c, ψ is a penalty function with polynomial growth and TV( Y, [0, T]) denotes the total variation of the process Y on the interval [0, T], Next, we apply obtained estimates in three specific cases: Brownian motion with drift on ℝ, standard Brownian motion on ℝ d and a symmetric α-stable process (α ∈ (1, 2)) on ℝ.
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