Statements (56)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:machine_learning
mathematical finance option pricing queueing theory statistical inference randomized algorithms risk-neutral measure gambling theory stochastic integration filtering theory stopping times |
| gptkbp:category |
gptkb:probability_theory
mathematical finance stochastic processes |
| gptkbp:defines |
A sequence of random variables where the expected value of the next value, given all prior values, is equal to the present value.
|
| gptkbp:field |
gptkb:probability_theory
|
| gptkbp:generalizes |
random walk
|
| gptkbp:hasType |
submartingale
supermartingale continuous-time martingale discrete-time martingale |
| https://www.w3.org/2000/01/rdf-schema#label |
Martingales
|
| gptkbp:importantFor |
gptkb:Doob's_martingale_convergence_theorem
gptkb:Doob's_maximal_inequality Martingale representation theorem Optional stopping theorem |
| gptkbp:introduced |
gptkb:Paul_Lévy
|
| gptkbp:property |
fair game
|
| gptkbp:relatedConcept |
gptkb:Itô_calculus
gptkb:stochastic_process gptkb:law_of_large_numbers ergodic theory measure theory variance random variable sigma-algebra independent increments stationary process expectation filtration stopping time probability space conditional expectation adapted process zero drift |
| gptkbp:relatedTo |
Brownian motion
Markov chain |
| gptkbp:usedIn |
finance
mathematical analysis statistics stochastic processes |
| gptkbp:bfsParent |
gptkb:Stochastic_Integrals
gptkb:Half_Moon_Light gptkb:Diffusions,_Markov_Processes,_and_Martingales |
| gptkbp:bfsLayer |
8
|