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Hoeffding has shown that tail bounds on the distribution for sampling from a finite population with replacement also apply to the corresponding cases of sampling without replacement.
Marginal structural models were introduced in order to provide estimates of causal effects from interventions based on observational studies in epidemiological research. We present a variant of the ...
Weak martingale Hardy spaces generated by an operator T are investigated. The concept of weak atoms is introduced and an atomic decomposition of the space wW; is given if the operator T is predicta...
Let (X(t); f E N') be a random sequence adopted to . a filtration (Ft)in (a,F ,P ) satisfying some natural assumption. If none of the events (X (t + 1) > X (t)), (X (t + 1) < X (t)) can be predicted...
By a classical result of P. Lbvy, the Brownian motion (Btjtb0 on R may be characterized as a continuous process on R such that (B,),,, and (3;-t),,, are martingales. Generalizations of this result ...
This is an expository review paper elaborating on the proof of the martingale functional central limit theorem (FCLT). This paper also reviews tightness and stochastic boundedness, highlighting one-di...
This is an expository review paper illustrating the “martin- gale method” for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximatio...
We show how the Clark-Ocone-Haussmann formula for Brownian motion on a compact Riemannian manifold put forward by S. Fang in his proof of the spectral gap inequality for the Ornstein-Uhlenbeck operato...
We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.
We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.
Let X be a Banach space. Suppose that for all p in (1, ∞) a constant Cp,X depending only on X and p exists such that for any two X-valued martingales f and g with tangent martingale difference sequenc...
Given a set-valued stochastic process (Vt)t=0,...,T, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors ξt in Vt, admitting an equivalent marting...
We give a simple probabilistic proof of the classical fact from complex analysis that the zeros of a holomorphic function of several variables are never isolated and that they are not contained in any...

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