In general, however, stochastic processes used in finance exhibit the Markov property, which mainly says that tomorrow’s value of the process only depends on today’s state of the process, and not any other more “historic” state or even the whole path history. The process then is also called memoryless.

The most common interpretation of Bayes’ formula in finance is the diachronic interpretation. This mainly states that over time we learn new information about certain variables or parameters of interest, like the mean return of a time series.

we assume that the regression parameters are not only random and distributed in some fashion, but that they follow some kind of random walk over time. It is the same generalization used when making the transition in finance theory from random variables to stochastic processes (which are essentially ordered sequences of random variables):