Properties of Expectations of Functions of Martingale Diffusions
| dc.creator | Lowther, George | |
| dc.date | 2008-01-02 | |
| dc.date.accessioned | 2026-07-07T08:52:06Z | |
| dc.date.available | 2026-07-07T08:52:06Z | |
| dc.description | Given a real valued and time-inhomogeneous martingale diffusion X, we investigate the properties of functions defined by the conditional expectation f(t,X_t)=E[g(X_T)|F_t]. We show that whenever g is monotonic or Lipschitz continuous then f(t,x) will also be monotonic or Lipschitz continuous in x. If g is convex then f(t,x) will be convex in x and decreasing in t. We also define the marginal support of a process and show that it almost surely contains the paths of the process. Although f need not be jointly continuous, we show that it will be continuous on the marginal support of X. We prove these results for a generalization of diffusion processes that we call `almost-continuous diffusions', and includes all continuous and strong Markov processes. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0801.0330 | |
| dc.identifier | http://arxiv.org/abs/0801.0330 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145167 | |
| dc.subject | Probability | |
| dc.subject | 60J60; 60J25; 60G44 | |
| dc.title | Properties of Expectations of Functions of Martingale Diffusions | |
| dc.type | text |