Supermartingale

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. 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 \]. In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) .. Every martingale is also a submartingale and a supermartingale. Conversely, any stochastic process that is both a submartingale and a  ‎ History · ‎ Definitions · ‎ Examples of martingales · ‎ Submartingales. In some cases, such as with Brownian motion, it is possible to explicitly construct the process to be continuous. Filtrations and Processes , Stochastic Calculus Notes — George Lowther First, the following statement applies to all quasimartingales as defined in these notes. Wiener-Prozess Sei ein Wiener-Prozess. See Google Help for more information. This can be differentiated to obtain the ordinary differential equation , which has the unique solution. Theorem 1 below provides us with cadlag versions under the condition that elementary integrals of the processes cannot, in a sense, get too large. Markow-Prozesse Wir zeigen nun, wie Martingale für Funktionen von Markow-Prozessen mit endlich vielen Zuständen konstruiert werden können. Similarly, the number of downcrossings, denoted by , is the supremum of the nonnegative integers such that there are times satisfying 1 and such that. Bei einem fairen Glücksspiel ist der Erwartungswert jedes Gewinns gleich null, d. Dann ergibt sich analog zur obigen Rechnung. That is, is bounded above by some finite value as runs through the positive reals. From Wikipedia, the free encyclopedia. PR , Stochastic Calculus , Stochastic Differential Equations , Supermartingale.