- ball. Similarly, if a
submartingale and a
martingale have
equivalent expectations for a
given time, the
history of the
submartingale tends to be bounded...
- Kolmogorov’s
submartingale inequality is a
result in the
study of
stochastic processes. It
gives a
bound on the
probability that a
submartingale exceeds any...
-
stochastic process X = (Xt)t∈ N {\displaystyle \mathbb {N} } 0 is a
submartingale or a
supermartingale and one of the
above conditions holds, then E [...
- \left(-{\frac {2\epsilon ^{2}}{\sum _{t=1}^{n}c_{t}^{2}}}\right).}
Since a
submartingale is a
supermartingale with
signs reversed, we have if
instead { X 0 ...
-
theorem in
stochastic calculus stating the
conditions under which a
submartingale may be
decomposed in a
unique way as the sum of a
martingale and an...
- supermartingale, and
every local martingale that is
bounded from
above is a
submartingale; however, a
local martingale is not in
general a martingale, because...
-
bounded monotone sequence converges.
There are
symmetric results for
submartingales,
which are
analogous to non-decreasing sequences. A
common formulation...
- last value, then it is
called a
submartingale. Thus, a
supermartingale represents an
unfavorable game and a
submartingale a
favorable game.
These names...
-
variation [M] in the Itô isometry, the use of the Doléans
measure for
submartingales, or the use of the Burkholder–Davis–Gundy
inequalities instead of the...
-
there that he
derived his
famous theorem on the
decomposition of a
submartingale, now
known as the Doob–Meyer decomposition.
After his
return to France...
