A general non-existence result for linear BSDEs driven by Gaussian processes. (English) Zbl 1358.60054
Summary: In this paper, we study linear backward stochastic differential equations driven by a class of centered Gaussian non-martingales, including fractional Brownian motion with Hurst parameter \(H \in (0,1) \setminus \{ \frac{1}{2} \}\). We show that, for every choice of deterministic coefficient functions, there is a square integrable terminal condition such that the equation has no solution.
MSC:
| 60G15 | Gaussian processes |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
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