Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156493 | Stochastic Processes and their Applications | 2015 | 21 Pages |
Abstract
We give meaning to differential equations with a rough path term and a Brownian noise term and study their regularity, that is we are interested in equations of the type Stη=S0+∫0ta(Srη)dr+∫0tb(Srη)∘dBr+∫0tc(Srη)dηr where η is a deterministic geometric, step-22 rough path and BB is a multi-dimensional Brownian motion. We then give two applications: a Feynman–Kac formula for RPDEs and a robust version of the conditional expectation that appears in the nonlinear filtering problem. En passant, we revisit the recent integrability estimates of Cass et al. (2013) for rough differential equations with Gaussian driving signals which might be of independent interest.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Joscha Diehl, Harald Oberhauser, Sebastian Riedel,