Universal Journal of Mathematics and Mathematical Sciences
Volume 1, Issue 2, Pages 83 - 105
(April 2012)
|
|
SDEs DRIVEN BY SDE SOLUTIONS
Alexander Schnurr
|
Abstract: We consider stochastic differential equations (SDEs) driven by Feller processes which are themselves solutions of multivariate Lévy driven SDEs. The solutions of these ‘iterated SDEs’ are shown to be non-Markovian. However, the process consisting of the driving process and the solution is Markov and even Feller in the case of bounded coefficients. The generator as well as the semimartingale characteristics of this process are calculated explicitly and fine properties of the solution are derived via the probabilistic symbol. A short simulation study and an outlook in the direction of stochastic modeling round out the paper. |
Keywords and phrases: fine properties, Ito process, stochastic differential equation, symbol.
Communicated by Lidia Filus |
|
Number of Downloads: 232 | Number of Views: 390 |
|