The Time Change Method and SDEs with Nonnegative Drift

• Autores: V.P. Kurenok
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 53, Nº 3, 2010, págs. 503-515
• Idioma: inglés
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• Resumen

  • Using the time change method we show how to construct a solution to the stochastic equation dXt=b(Xt-)dZt+a(Xt)dt with a nonnegative drift a provided there exists a solution to the auxililary equation dLt=[a-1/ab](Lt-)d?Zt+dt where Z, ?Z are two symmetric stable processes of the same index a ? (0,2]. This approach allows us to prove the existence of solutions for both stochastic equations for the values 0 < a < 1 and only measurable coefficients a and b satisfying some conditions of boundedness. The existence proof for the auxililary equation uses the method of integral estimates in the sense of Krylov.