On solutions of one-dimensional stochastic differential equations driven by stable Lévy motion

DOI10.1016/S0304-4149(97)00030-6zbMath0911.60037MaRDI QIDQ1275927

Pio Andrea Zanzotto

Publication date: 14 January 1999

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

existencestochastic differential equationstime changezero-one lawrandom measures\(\alpha \)-stable Lévy motions``local existencepurely discontinuous martingalesstable integrals

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

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Cites Work

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• Calcul stochastique et problèmes de martingales
• On the martingale problem for generators of stable processes with perturbations
• On Itô stochastic integration with respect to p-stable motion: Inner clock, integrability of sample paths, double and multiple integrals
• Some time change representations of stable integrals, via predictable transformations of local martingales
• Local times for a class of Markoff processes
• Hitting times and potentials for recurrent stable processes
• The set of zeros of a semistable process
• On solutions of one-dimensional stochastic differential equations without drift
• Hitting probabilities of single points for processes with stationary independent increments