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In this thesis we study the central limit theorem (CLT) for nonuniformly hy- perbolic dynamical systems. We examine cases in which polynomial decay of cor- relations leads to a CLT with a non-standard...
In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching rand...
This paper constructs a class of martingale transforms based on L\'evy processes on Lie groups. From these, a natural class of bounded linear operators on the $L^p$-spaces of the group (with respect t...
We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\eps$, agrees up to generation $K$ with a regular $\mu$-ary tree, where $\mu$ is the essential mini...
Abstract: 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. (A spec...
Let L be a linear space of real bounded random variables on the probability space ( ,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L.
We prove the uniqueness of the martingale problem associated to some degenerate operators. The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins (Fr...
The principle of minimization of relative entropy is used to construct a minimal entropy martingale measure for a finite probability/multiperiod market model.
We study (local) martingale problems on a general separable Banach space E and apply our results to stochastic evolution equations. In particular,we prove that if such an equation is well-posed, then ...
In the context of Markovian evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a ...
We consider a Poisson process $\eta$ on a measurable space $(\BY,\mathcal{Y})$ equipped with a partial ordering, assumed to be strict almost everwhwere with respect to the intensity measure $\lambda$ ...
An exchange option allows its holder to exchange one asset for another at maturity. In this short paper, the martingale approach, which is based on Continuous martingale representation theorem and Gir...
A result is found which is similar to BDG-inequalities, but in the framework of exponential (non moderate) Orlicz spaces. A special class of such spaces is introduced and its properties are discussed ...
In this article, the problem of real options valuation in multinomial trees is investigated. A concrete single real options value based on the minimal entropy martingale measure is provided. Using the...
In this paper, we will establish a martingale inequality, which extends the classic Hoeffding inequality in some sense. In addition, our inequality improves the results of Lee and Su [7] (2002) in som...

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