measurability of stochastic processes
For a continuous-time stochastic process adapted to a given filtration (http://planetmath.org/FiltrationOfSigmaAlgebras) on a measurable space , there are various conditions which can be placed either on its sample paths or on its measurability when considered as a function from to . The following theorem lists the dependencies between these properties.
Let be a real valued stochastic process. Then, is optional if it is adapted and right-continuous, it is predictable if it is adapted and left-continuous. Furthermore, each of the following properties implies the next.
is adapted and jointly measurable.
|Title||measurability of stochastic processes|
|Date of creation||2013-03-22 18:37:29|
|Last modified on||2013-03-22 18:37:29|
|Last modified by||gel (22282)|