-
called a
semimartingale if it can be
decomposed as the sum of a
local martingale and a càdlàg
adapted finite-variation process.
Semimartingales are "good...
- with the
operation of
taking quadratic covariations. If X and Y are
semimartingales then any X-integrable
process will also be [X, Y]-integrable, and [H...
- _{0}^{t}\sigma _{s}^{2}\,ds.}
Quadratic variations and
covariations of all
semimartingales can be
shown to exist. They form an
important part of the
theory of...
- in die
Theorie der
stetigen Semimartingale [Stochastic Analysis: An
introduction to the
theory of
continuous semimartingales], pp. 349–544, ISBN 978-3-519-02229-9...
-
calculation of
characteristic functions. Yor's formula: for any two
semimartingales U {\displaystyle U} and V {\displaystyle V} one has E ( U ) E ( V )...
-
generally a
semimartingale. However,
other types of
random behaviour are possible, such as jump
processes like Lévy
processes or
semimartingales with jumps...
-
integral or Fisk–Stratonovich
integral of a
semimartingale X {\displaystyle X}
against another semimartingale Y can be
defined in
terms of the Itô integral...
- be
applied to
general d-dimensional
semimartingales,
which need not be continuous. In general, a
semimartingale is a càdlàg process, and an additional...
- predictability. The
theory also
extends Itô's
theory of SDEs far
beyond the
semimartingale setting. At the
heart of the
mathematics is the
challenge of describing...
-
martingales holds also for
local martingales. A wide
class of
continuous semimartingales (especially, of
diffusion processes) is
related to the
Wiener process...
