Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1154562 | Statistics & Probability Letters | 2008 | 9 Pages |
Abstract
The one-dimensional stochastic equation dXt=b1(Xt)dWt+b2(Xtâ)dZt+a(Xt)dt,tâ¥0, where b1,b2,a:RâR are Borel measurable functions, W is a Brownian motion, and Z is a symmetric stable process of index 0<α<2, is considered. We prove the existence of (weak) solutions under some conditions of boundedness of coefficients when b1 can be degenerate which improves the results of Lepeltier and Marchal [Lepeltier, J.P., Marchal, B., 1976. Probléme des martingales et équations différentielles stochastiques associées á un opérateur intégro-différentiel. Ann. IHP 12 (1), 43-103] for this case. Our approach is based on Krylov's estimates for solutions X and the weak convergence arguments.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
V.P. Kurenok,