Mathematics – Probability
Scientific paper
2009-06-29
Mathematics
Probability
27 pages; typos corrected
Scientific paper
10.1007/s10959-010-0320-9
It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct consequence, a specialized form of the Ito formula is derived. When a standard Brownian motion is the original semimartingale, classical Ito stochastic differential equations driven by the Brownian motion with drift extend to a larger class of stochastic differential equations involving a time-change with continuous paths. A form of the general solution of linear equations in this new class is established, followed by consideration of some examples analogous to the classical equations. Through these examples, each coefficient of the stochastic differential equations in the new class is given meaning. The new feature is the coexistence of a usual drift term along with a term related to the time-change.
No associations
LandOfFree
Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-439968