- 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...
- We will
prove the
supermartingale case only as the rest are self-evident. By Doob decomposition, we
could decompose supermartingale { X t } {\displaystyle...
- = (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 ] ...
- D" to
refer to the
class of
supermartingales for
which his
unique decomposition theorem applied. A càdlàg
supermartingale Z {\displaystyle Z} is of class...
- Ville's
inequality provides an
upper bound on the
probability that a
supermartingale exceeds a
certain value. The
inequality is
named after Jean Ville,...
- envelope, used in
stochastics and
mathematical finance, is the
smallest supermartingale dominating a
stochastic process. The
Snell envelope is
named after...
-
process Doob–Meyer
decomposition theorem of a continuous-time sub- or
supermartingale Fourier decomposition, re-expressing a
given periodic function as the...
- theorem) is a
mathematical theorem on the
decomposition of a
positive supermartingale V {\displaystyle V} with
respect to a
family of
equivalent martingale...
- particular,
every local martingale that is
bounded from
below is a
supermartingale, and
every local martingale that is
bounded from
above is a submartingale;...
