# Supermartingale

Definition Let (il, F, P) be a probability triple and {Tt} be a filtration on F. A stochastic process X is an {Ft} supermartingale if: (i) X is adapted to \Tt } ; (ii) E[\Xt \]. Submartingale und Supermartingale ; Beispiele. Definition: \$ \;\$ Sei \$ \{X_t,\,t\ge 0 \}\$ ein stochastischer Prozess über dem. it is called a super-martingale. An important result is Jensen's inequality. Theorem. If Xn is a martingale and if φ(x) is a convex function of x then φ(Xn) = Yn is.

### Video

Martingales AnastasisKratsios on The Projection Theorems. Definition 1 A martingale,is an integrable process satisfying. Casino verweigert auszahlung Sei ein Wiener-Prozess. Whereas constructing examples of local martingales which are not martingales is a relatively straightforward exercise, such examples are often slightly contrived and the martingale property fails for obvious reasons e. Martingale und Martingaltheorie Satz Stochastik. This would indeed follow if it was known that it is a martingale, as is often assumed to be true for stochastic integrals with respect to Brownian motion. In fact, the following inequality holds 4 almost surely for times.

### Supermartingale - letztes

PR , Stochastic Calculus , Stochastic Differential Equations , Supermartingale. This therefore describes a fair game where, eventually, the gambler is guaranteed to win. Dann ergibt sich analog zur obigen Rechnung. This is therefore a martingale, showing that is a local martingale. That is, the conditional expected value of the next observation, given all the past observations, is equal to the most recent observation.