Maximal inequalities and weighted BMO processes
@inproceedings{Le2022MaximalIA, title={Maximal inequalities and weighted BMO processes}, author={Khoa Le}, year={2022} }
. For a general adapted integrable right-continuous with left limits (RCLL) process ( π π‘ ) π‘ β[ 0 ,π ] taking values in a metric space (E ,π ) , we show (among other things) that for every π β ( 1 , βΒ
References
SHOWING 1-10 OF 36 REFERENCES
Sharp maximal estimates for BMO martingales
- Mathematics
- 2015
We introduce a method which can be used to study maximal inequalities for martingales of bounded mean oscillation. As an application, we establish sharp Ξ¦-inequalities and tail inequalities for theβ¦
Quantifying a convergence theorem of Gy\"ongy and Krylov
- Mathematics
- 2021
We derive sharp strong convergence rates for the EulerβMaruyama scheme approximating multidimensional SDEs with multiplicative noise without im-posing any regularity condition on the driftβ¦
Multidimensional Diffusion Processes
- Mathematics
- 1979
Preliminary Material: Extension Theorems, Martingales, and Compactness.- Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure.- Parabolic Partial Differential Equations.- Theβ¦
Quantitative John--Nirenberg inequality for stochastic processes of bounded mean oscillation
- Mathematics
- 2022
. Stroock and Varadhan in 1997 and Geiss in 2005 independently introduced stochastic processes with bounded mean oscillation (BMO) and established their exponential integrability with some unspeciο¬edβ¦
On the intergrability of the martingale square function
- Mathematics
- 1970
AbstractLetf=(f1,f2,..) be a martingale. It is proved that theL1 norms of supn|fn| and of
$$\left( {\sum {\left( {f_n - f_{n - 1} } \right)^2 } } \right)^{\tfrac{1}{2}} $$
are equivalent. Thisβ¦
Weighted BMO and discrete time hedging within the Black-Scholes model
- Mathematics
- 2005
Abstract.The paper combines two objects rather different at first glance: spaces of stochastic processes having weighted bounded mean oscillation (weighted BMO) and the approximation of certainβ¦
A stochastic sewing lemma and applications
- MathematicsElectronic Journal of Probability
- 2020
We introduce a stochastic version of Gubinelli's sewing lemma, providing a sufficient condition for the convergence in moments of some random Riemann sums. Compared with the deterministic sewingβ¦
Maximal Inequalities and Some Applications
- Mathematics
- 2022
A maximal inequality is an inequality which involves the (absolute) supremum $\sup_{s\leq t}|X_{s}|$ or the running maximum $\sup_{s\leq t}X_{s}$ of a stochastic process $(X_t)_{t\geq 0}$. We discussβ¦
Integral Inequalities for Convex Functions of Operators on Martingales
- Mathematics
- 2011
Let M be a family of martingales on a probability space (Ξ©, A, P) and let Ρ be a nonnegative function on [0, β]. The general question underlying both [2] and the present work may be stated as followsβ¦
Stochastic sewing in Banach space
- Mathematics
- 2021
The sewing lemma is an instrumental and versatile tool originated from Lyonsβ theory of rough paths [Lyo98]. A specific case of the lemma can be traced back at least to the work [You36] of Young onβ¦