Abstract
Set-indexed local martingales are defined and studied. We present some optional sampling theorems for strong martingales, martingales and weak martingales. The class of set-indexed processes which are locally of class (D) is introduced. A Doob-Meyer decomposition is obtained: any local weak submartingale has a unique decomposition into the sum of a local weak martingale and a local predictable increasing process. Finally some examples are given.
| Original language | English |
|---|---|
| Pages (from-to) | 83-98 |
| Number of pages | 16 |
| Journal | Stochastic Processes and their Applications |
| Volume | 57 |
| Issue number | 1 |
| DOIs | |
| State | Published - May 1995 |
Bibliographical note
Funding Information:*Corresponding author. E-mail: [email protected]. Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada. 2Work done during a visit at the University of Ottawa. The second author wishes to thank Professor Ivanoff for her hospitality.
Funding
*Corresponding author. E-mail: [email protected]. Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada. 2Work done during a visit at the University of Ottawa. The second author wishes to thank Professor Ivanoff for her hospitality.
| Funders | Funder number |
|---|---|
| Natural Sciences and Engineering Research Council of Canada |
Keywords
- Class (D)
- Doob-Meyer decomposition
- Lattice
- Local martingale
- Optional sampling
- Predictable σ-algebra
- Set-indexed martingale
- Stopping set
- Submartingale