Notation

\fs4 \mathscr{A}Diffusion generator
\fs4 E[X], EXexpectation
\fs4 E[X|\mathscr{F}]conditional expectation
\fs4 \mathscr{F}, \mathscr{G}sigma algebra
\fs4 \mathscr{F}_X, \mathscr{F}_{\mathscr{G}}generated sigma algebra
\fs4 P, Qprobability measure
\fs4 P[X|\mathscr{F}]conditional probability
\fs4 P\ll Qabsolutely continuous measures
\fs4 P\sim Qequivalent probability measures
\fs4 X, Yrandom variable
\fs4 X_t, X_t(\omega), X(t,\omega)stochastic process
\fs4 \OmegaSample space
\fs4 (\Omega, \mathscr{F})measure space
\fs4 (\Omega, \mathscr{F}, P)probability space
\fs4 (\Omega, \mathbb{F}, \mathscr{F}, P)filtered space


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