Chapter 63: Structural alterations
631
Near-simple processes
Near-simple processes; and càdlàg sample paths; the spaces
Mn-s and Mln-s; indefinite integrals; quadratic variation,
bounded variation, cumulative variation; a general extension method
for near-simple processes; stopping lemmas; saltus and oscillation.
632
Right-continuous filtrations
Right-continuous filtrations; near-simple processes; local and
virtually local martingales; càdlàg processes; the Poisson
process.
633
Separating sublattices
Separating sublattices; cases when
∫Su dv=∫S′u dv;
connections between properties of a process and its restriction to a
separating sublattice; continuous-time structures.
634
Changing the algebra
Subalgebras, restricted filtrations and induced stochastic
integration structures; fully adapted processes and absolute
properties; relative independence and subalgebras coordinated with
filtrations; martingales; stochastic independence and free products.
635
Changing the filtration
The filtration defined by a totally ordered family of stopping times;
the corresponding transformation of fully adapted processes;
integration by substitution; quadratic variations.
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