Category:Adapted Stochastic Process is Martingale iff Supermartingale and Submartingale
This category contains pages concerning Adapted Stochastic Process is Martingale iff Supermartingale and Submartingale:
Discrete Time
Let $\struct {\Omega, \Sigma, \sequence {\FF_n}_{n \mathop \ge 0}, \Pr}$ be a discrete-time filtered probability space.
Let $\sequence {X_n}_{n \mathop \ge 0}$ be a discrete-time $\sequence {\FF_n}_{n \mathop \ge 0}$-adapted stochastic process.
Then $\sequence {X_n}_{n \mathop \ge 0}$ is a $\sequence {\FF_n}_{n \mathop \ge 0}$-martingale if and only if it is a $\sequence {\FF_n}_{n \mathop \ge 0}$-supermartingale and a $\sequence {\FF_n}_{n \mathop \ge 0}$-submartingale.
Continuous Time
Let $\struct {\Omega, \Sigma, \sequence {\FF_t}_{t \ge 0}, \Pr}$ be a continuous-time filtered probability space.
Let $\sequence {X_t}_{t \ge 0}$ be a continuous-time $\sequence {\FF_t}_{t \ge 0}$-adapted stochastic process.
Then $\sequence {X_t}_{t \ge 0}$ is a $\sequence {\FF_t}_{t \ge 0}$-martingale if and only if it is a $\sequence {\FF_t}_{t \ge 0}$-supermartingale and a $\sequence {\FF_t}_{t \ge 0}$-submartingale.
Pages in category "Adapted Stochastic Process is Martingale iff Supermartingale and Submartingale"
The following 3 pages are in this category, out of 3 total.