On differentiability with respect to the initial data of the solution to an SDE with a Lévy noise and discontinuous coefficients
We construct a stochastic flow generated by an stochastic differential equation with its drift being a function of bounded variation and its noise being a stable process with exponent from (1,2). It is proved that the flow is non-coalescing and Sobolev differentiable with respect to
the initial data. The representation for the derivative is given.
Keywords: 60H10; 60J65; differentiability with respect to initial data; local time; stable process; stochastic flow
Document Type: Research Article
Affiliations: 1: Institute of Geophysics, National Academy of Sciences of Ukraine, Palladin pr. 32, 03680, Kiev-142, Ukraine 2: Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska str. 3, 01601, Kiev, Ukraine
Publication date: 04 July 2014
- Access Key
- Free content
- Partial Free content
- New content
- Open access content
- Partial Open access content
- Subscribed content
- Partial Subscribed content
- Free trial content