Abstract
In this paper we extend an inequality of Lenglart et al. (1980, Lemma 1.1) to general continuous adapted stochastic processes with values in topological spaces. Using this inequality we prove Burkholder–Davies–Gundy's inequality for stochastic integrals in Orlicz-type spaces (a class of quasi-Banach spaces) with respect to cylindrical Brownian motions. As an application, we show the well-posedness of stochastic heat equations in Orlicz spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 3228-3250 |
| Number of pages | 23 |
| Journal | Stochastic Processes and their Applications |
| Volume | 127 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - Oct 2017 |
| Externally published | Yes |
Keywords
- BDG's inequality
- Good λ-inequality
- Orlicz space
- Quasi-Banach space
- Regularly varying function
- Stochastic integral
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Xie, Y., & Zhang, X. (2017). Stochastic integrals and BDG's inequalities in Orlicz-type spaces. Stochastic Processes and their Applications, 127(10), 3228-3250. https://doi.org/10.1016/j.spa.2017.02.006