  Invariance times are stopping times $\tau$ such that local martingales with
respect to some reduced filtration and an equivalently changed probability
measure, stopped before $\tau$ , are local martingales with respect to the
original model filtration and probability measure. They arise naturally for
modeling the default time of a dealer bank, in the mathematical finance context
of counterparty credit risk. Assuming an invariance time endowed with an
intensity and a positive Az{\'e}ma supermartingale, this work establishes a
dictionary relating the semimartingale calculi in the original and reduced
stochastic bases, regarding in particular conditional expectations,
martingales, stochastic integrals, random measure stochastic integrals,
martingale representation properties, semimartingale characteristics, Markov
properties, transition semigroups and infinitesimal generators, and solutions
of backward stochastic differential equations.
