- 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...
- envelope, used in
stochastics and
mathematical finance, is the
smallest supermartingale dominating a
stochastic process. The
Snell envelope is
named after...
- D" to
refer to the
class of
supermartingales for
which his
unique decomposition theorem applied. A càdlàg
supermartingale Z {\displaystyle Z} is of class...
- 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,...
- = (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 ] ...
- particular,
every local martingale that is
bounded from
below is a
supermartingale, and
every local martingale that is
bounded from
above is a submartingale;...
-
integrable predictable process A that is
almost surely increasing. It is a
supermartingale, if and only if A is
almost surely decreasing. If X is a submartingale...
-
process is a
supermartingale and, if it is
greater than or
equal to the last value, then it is
called a submartingale. Thus, a
supermartingale represents...
