Chapter 61: The Riemann-sum integral

611
Stopping times

Filtrations; the lattice ** T** of stopping times; the regions
[[σ<τ]]; suprema and infima in

612
Fully adapted processes

*L*^{0} spaces; *f*-algebras of fully adapted processes; the identity
process; progressively measurable classical processes; actions of
Borel measurable real functions; simple processes; order-bounded
processes; extension of processes to covered envelopes; Brownian
motion; the Poisson process.

613
Definition of the integral

Convergence in measure; interval functions;
Δ_{e}(** u**,

614
Moderately oscillatory processes

The ucp topology on *M*_{ob}; moderately oscillatory processes;
approximating a moderately oscillatory process; near-simple
processes; classical processes with càdlàg sample paths.

615
Integrators

Capped-stake variation sets; integrators; integration and the ucp
topology; if ** u** is moderately oscillatory and

616
Integral identities and quadratic variations

Indefinite integrals are integrators; integrating with respect to an
indefinite integral; covariation and quadratic variation;
integrating with respect to a covariation; calculating the quadratic
variation of the identity process and the Poisson process.

617
Jump-free processes

Oscillations; jump-free processes; classical processes with
continous sample paths.

618
Itô's formula

Itô's formula in one dimension; *k*-tuples of processes; Itô's
formula in *k* dimensions.

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Revised 4.3.2018