Resumen de The Time Change Method and SDEs with Nonnegative Drift

V.P. Kurenok

• 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.