Filtrationskällan

Filtrationskällan is a Swedish term that designates the underlying source or mechanism that generates a filtration in probability theory, i.e., the evolving body of information available over time. In formal terms, a filtration is an increasing family of sigma-algebras F_t on a probability space (Ω, F, P), indexed by t in a time set. The filtrationskällan is the process or data stream that determines these sigma-algebras; for a stochastic process X_t, the natural filtration is F_t = σ(X_s : s ≤ t). This captures all events that can be determined by observations up to time t.

Examples include a Brownian motion, which generates the standard natural filtration, or a Poisson process with its jump times. In multivariate settings, the filtration may be generated by several processes or by a combination of observations.

Uses: Filtrationskällan plays a central role in modeling information flow in stochastic modeling, finance, and control. They underpin definitions of adapted processes, stopping times, and martingales, and they are essential for formulating problems in pricing, hedging, and optimal stopping where decisions depend on available information.

Notes: The term filtrationskällan is not a universally standard technical label; it is typically described in Swedish texts as the source of the filtration, i.e., the process or data stream that defines F_t.