- Similarly, if a
supermartingale and a
martingale have
equivalent expectations for a
given time, the
history of the
supermartingale tends to be bounded...
- the
result that any
supermartingale satisfying a
certain boundedness condition must converge. One may
think of
supermartingales as the
random variable...
- D" to
refer to the
class of
supermartingales for
which his
unique decomposition theorem applied. A càdlàg
supermartingale Z {\displaystyle Z} is of class...
-
generalizations of test
supermartingales,
which are
nonnegative supermartingales with
starting value 1: any test
supermartingale constitutes an e-process...
- processes,
Brownian motion and
Poisson processes).
Submartingales and
supermartingales together represent a
subset of the semimartingales. A real
valued process...
- ISBN 3-540-63929-2. Dellacherie, C.; Meyer, P.-A. (1982). "Decomposition of
Supermartingales, Applications".
Probabilities and Potential. Vol. B.
Translated by...
- = (Xt)t∈ N {\displaystyle \mathbb {N} } 0 is a
submartingale or a
supermartingale and one of the
above conditions holds, then E [ X τ ] ≥ E [ X 0 ] ...
- We will
prove the
supermartingale case only as the rest are self-evident. By Doob decomposition, we
could decompose supermartingale { X t } {\displaystyle...
- Ville's
inequality provides an
upper bound on the
probability that a
supermartingale exceeds a
certain value. The
inequality is
named after Jean Ville,...
-
equivalent measure. Kramkov,
Dimitri O. (1996). "Optional
decomposition of
supermartingales and
hedging contingent claims in
incomplete security markets". Probability...
