On the Exact Asymptotics of Exit Time From a Cone of an Isotropic α-Self-Similar Markov Process with a Skew-Product Structure

• Autorzy: Palmowski Zbigniew , Wang Longmin

Identyfikatory

DOI

10.37190/0208-4147.41.1.3

• Języki publikacji: EN

Abstrakty

EN

In this paper we identify the asymptotic tail of the distribution of the exit time τ_C from a cone C of an isotropic α-self-similar Markov process X_t with a skew-product structure, that is, X_t is a product of its radial process and an independent time changed angular component θ_t. Under some additional regularity assumptions, the angular process θ_t killed on exiting the cone C has a transition density that can be expressed in terms of a complete set of orthogonal eigenfunctions with corresponding eigenvalues of an appropriate generator. Using this fact and some asymptotic properties of the exponential functional of a killed Lévy process related to the Lamperti representation of the radial process, we prove that P_x(τ_C> t) ~h(x)t^-k1 as t→∞ for h and k₁ identified explicitly. The result extends the work of De Blassie (1988) and Bañuelos and Smits (1997) concerning the Brownian motion.

Słowa kluczowe

EN

α-self-similar process; cone; exit time; skew-product structure; Lamperti representation; exponential functional; Brownian motion

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2021
• Tom: Vol. 41, Fasc. 1
• Strony: 25--38
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Palmowski Zbigniew

• Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Wang Longmin

• School of Mathematical Sciences, Nankai University, Tianjin 300071, P.R. China

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).