Common · Knowledge
Semimartingale
Type of stochastic process
In probability theory, a real-valued stochastic process X is called a semimartingale if it can be decomposed as the sum of a local martingale and an adapted finite-variation process whose paths are right-continuous with left limits (càdlàg). Semimartingales are "good integrators", forming the largest class of processes with respect to which the Itô integral and the Stratonovich integral can be defined.
From Wikipedia
In probability theory, a real-valued stochastic process X is called a semimartingale if it can be decomposed as the sum of a local martingale and an adapted finite-variation process whose paths are right-continuous with left limits (càdlàg). Semimartingales are "good integrators", forming the largest class of processes with respect to which the Itô integral and the Stratonovich integral can be defined. The class of semimartingales is quite large (including, for example, all continuously differentiable processes, Brownian motion and Poisson processes). Submartingales and supermartingales together represent a subset of the semimartingales.
Text: Wikipédia, CC BY-SA 4.0. ·
Related cards
-
★★★
Martingale (probability theory)
Model in probability theory, used in gambling
-
O★
Optional stopping theorem
Martingale's expected value at a stopping time equals its initial expected value
-
A★
Azuma's inequality
Probabilistic inequality applying to martingales with bounded differences
-
★★★
Ornstein–Uhlenbeck process
Stochastic process with applications in financial mathematics and the physical sciences
-
★
Bounded variation
Real function with finite total variation
-
★
Bessel process
Mathematical process for stochastic differential equations