Stochastic Equations Driven by a Cauchy Process
| Autor: | V. P. Kurenok |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Stewart N. Ethier, Jin Feng and Richard H. Stockbridge, eds., Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 99-106 |
| DOI: | 10.1214/074921708000000327 |
| Popis: | Using the method of Krylov’s estimates, we prove the existence of (weak) solutions of the one-dimensional stochastic equation dXt=b(Xt−)dZt+a(Xt)dt with arbitrary initial value x0∈ℝ and the driven symmetric Cauchy process Z. The bounded coefficient b is assumed to be of non-degenerate form and the drift a to satisfy the condition |a(x)|≤(1/2)|b(x)| for all x∈ℝ. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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