caa a22 4500 463177177 CHVBK 20180406164828.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s10986-007-0030-x doi (NATIONALLICENCE)springer-10.1007/s10986-007-0030-x Kurenok V. Department of Natural and Applied Sciences, University of Wisconsin-Green Bay, 2420 Nicolet Drive, 54311-7001, Green Bay, WI, USA aut On driftless one-dimensional SDE's with respect to stable Levy processes [Elektronische Daten] [V. Kurenok] The time-dependent SDE dX t = b(t, X t−)dZ t with X 0 = x 0 ∈ ℝ, and a symmetric α-stable process Z, 1 < α ⩽ 2, is considered. We study the existence of nonexploding solutions of the given equation through the existence of solutions of the equation $$dA_t = \left| b \right|^\alpha (t,\bar Z \circ A_t )dt$$ in class of time change processes, where $$\bar Z$$ is a symmetric stable process of the same index α as Z. The approach is based on using the time change method, Krylov's estimates for stable integrals, and properties of monotone convergence. The main existence result extends the results of Pragarauskas and Zanzotto (2000) for 1 < α < 2 and those of T. Senf (1993) for α = 2. Springer Science+Business Media, Inc., 2007 one-dimensional stochastic equations nationallicence measurable coefficients nationallicence symmetric stable processes nationallicence time change equation nationallicence monotone convergence nationallicence Lithuanian Mathematical Journal Springer US 47/4(2007-10-01), 423-435 0363-1672 47:4<423 2007 47 10986 https://doi.org/10.1007/s10986-007-0030-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10986-007-0030-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kurenok V. Department of Natural and Applied Sciences, University of Wisconsin-Green Bay, 2420 Nicolet Drive, 54311-7001, Green Bay, WI, USA aut NATIONALLICENCE 773 0- Lithuanian Mathematical Journal Springer US 47/4(2007-10-01), 423-435 0363-1672 47:4<423 2007 47 10986 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer