The Time Change Method and SDEs with Nonnegative Drift

Canadian mathematical bulletin

V. P. Kurenok¹ 

[1] Department of Natural and Applied Sciences, University of Wisconsin-Green Bay, Green Bay, WI, USA

关键词: One-dimensional SDEs;    symmetric stable processes;    nonnegative drift;    time change;    integral estimates;    weak convergence;   

DOI  :  10.4153/CMB-2010-048-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Using the time change method we show how to construct a solution to the stochastic equation $dX_t=b(X_{t-})dZ_t+a(X_t)dt$ with a nonnegative drift $a$ provided there exists a solution to the auxililary equation $dL_t=[a^{-1/alpha}b](L_{t-})dar Z_t+dt$ where $Z, ar Z$ are two symmetric stable processes of the same index $alphain(0,2]$. This approach allows us to prove the existence of solutions for both stochastic equations for the values $0

【 授权许可】

Unknown