- ball. Similarly, if a
submartingale and a
martingale have
equivalent expectations for a
given time, the
history of the
submartingale tends to be bounded...
-
valid for
submartingales. The
inequality is due to the
American mathematician Joseph L. Doob. The
setting of Doob's
inequality is a
submartingale relative...
-
continuous submartingales".
Theory of
Probability and Its Applications. 10 (3): 401–410. doi:10.1137/1110048. "On
decomposition of
continuous submartingales"....
-
inequalities Kolmogorov's
inequality Kolmogorov's
inequality for
positive submartingales In
functional analysis Landau–Kolmogorov
inequality Fréchet–Kolmogorov...
-
bounded monotone sequence converges.
There are
symmetric results for
submartingales,
which are
analogous to non-decreasing sequences. A
common formulation...
-
continuously differentiable processes,
Brownian motion and
Poisson processes).
Submartingales and
supermartingales together represent a
subset of the semimartingales...
-
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 [...
-
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...
- \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 ...
- supermartingale, and
every local martingale that is
bounded from
above is a
submartingale; however, a
local martingale is not in
general a martingale, because...
