Geodesic
The Time Change Method and SDEs with Nonnegative Drift
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 503-515

Voir la notice de l'article provenant de la source Cambridge University Press

Using the time change method we show how to construct a solution to the stochastic equation $d{{X}_{t}}\,=\,b({{X}_{t}}\_)d{{Z}_{t}}\,+\,a({{X}_{t}})dt$ with a nonnegative drift a provided there exists a solution to the auxililary equation $d{{L}_{t}}=[{{a}^{-1/\alpha }}b]({{L}_{t}}\_)d\overline{{{Z}_{t}}}+dt$ where $Z,\,\overline{Z}$ are two symmetric stable processes of the same index $\alpha \,\in \,(0,\,2]$ . This approach allows us to prove the existence of solutions for both stochastic equations for the values $0\,<\,\alpha \,<\,1$ 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.
DOI : 10.4153/CMB-2010-048-9
Mots-clés : 60H10, 60J60, 60J65, 60G44, One-dimensional SDEs, symmetric stable processes, nonnegative drift, time change, integral estimates, weak convergence 
Kurenok, V. P. The Time Change Method and SDEs with Nonnegative Drift. Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 503-515. doi: 10.4153/CMB-2010-048-9
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