Monotonicity and non-monotonicity of domains of stochastic integral operators

• Autorzy: Sato K.
• Języki publikacji: EN

Abstrakty

EN

A Lévy process on R^d with distribution }μ at time 1 is denoted by X^μ = {X^μ_t}, If the improper stochastic integral [formula] of f with respect to X^μ is definable, its distribution is denoted by Ф_∫(μ). The class of all infinitely divisible distributions μ on R^d such that Ф_∫(μ) is definable is denoted by D(Φ_∫). The class D(Φ_∫), its two extensions D_c(Φ_∫) and D_es(Φ_∫) (compensated and essential), and its restriction D⁰(Φ_∫)(absolutely definable) are studied. It is shown that D_es(Φ_∫) is monotonic with respect to ∫, which means that |f₂| ≤ |f₁| implies D_es(Φ_∫1) ⊂ D_es(Φ_∫2). Further D⁰Φ_f is monotonic with respect to ∫ but neither D(Φ_∫) nor D₀(Φ_∫)is monotonic with respect to ∫. Furthermore, there exist μ, ∫₁ and ∫₂ such that 0 ≤∫₂ ∫₁, and μ∈D(Φ_∫1), and μ ∉D(Φ_∫2) An explicit example for this is related to some properties of a class of martingale Levy processes.

Słowa kluczowe

EN

improper stochastic integral; infinitely divisible distribution; Lévy process; martingale Lévy process; monotonic

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2006
• Tom: Vol. 26, Fasc. 1
• Strony: 23--39
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Sato K.

• Hachiman-yama 1101-5-103, Tenpaku-ku Nagoya, 468-0074 Japan

Bibliografia

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