Doob inequality(Doob不等式) Lemma:X poisitive submartingale,∀p>1,n∈N,E(max0≤i≤nXip)≤(pp−1)pE(Xnp)Proof:Yn:=max1≤i≤nXi,for λ>0,τλ:=inf{0≤i≤n:Xi>λ},τλ=n+1,if{}=∅.⇒∑k=1n1{τλ=k}=1{Yn>λ},Ynp=∫0Ynpλp−1dλ=∫0∞λp−11{Yn>λ...
As an extension of the Doob-Meyer decomposition of a semimartingale and the Fukushima representation of a Dirichlet process, we introduce a general Doob decomposition in continuous time, where a square-integrable process is represented as the sum of a martingale and a process with "vanishing local...
Johnson, W.B., Schechtman, G.: Martingale inequalities in rearrangement invariant function spaces. Isr. J. Math. 64, 267–275 (1988) Article MathSciNet MATH Google Scholar Kikuchi, M.: Characterization of Banach function spaces that preserve the Burkholder square-function inequality. Il. J. ...
MartingaleMaximal inequalityRiesz systemStochastic integralLet X, Y be local martingales such that Y is differentially subordinate to X. The article contains the proof of the sharp estimatesdoi:10.1080/07362994.2012.668441Ose?kowskiAdamMarcel Dekker, Inc.Stochastic Analysis & Applications...
MartingaleMaximal inequalityRiesz systemStochastic integralLet X, Y be local martingales such that Y is differentially subordinate to X. The article contains the proof of the sharp estimatesAdam Ose¸kowskiDepartment of MathematicsStochastic Analysis and Applications...
With Doob decomposition of B-valued asymptotic martingale, studies the law of large numbers of B-valued asymptotic martingale, some results are obtained. 利用B值渐近鞅的Doob分解定理 ,研究了B值渐近鞅的大数定律 ,它们是鞅的有关结论的推广和改进 。 3. In this paper,with the Doob decomposition ...