I have a general question regarding the notion of "continuous martingale". Does this expression refer to a continuous time stochastic process that has the property of being a martingale or does it refer to a martingale that has continuous paths? I would say the first definition should be the one it refers to (the second it refers generally to BM only, right?) but I get unsure since some articles I am reading do not define the concept form the beginning.
2026-03-29 23:39:56.1774827596
Continuous martingale
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Usually, a stochastic process is called a continuous martingale if it is a martingale and has continuous sample paths. (Note that not any martingale with continuous sample paths is a Brownian motion.)