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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...
Streamflow forecasts are dynamically updated in real-time, thus facilitating a process of forecast uncertainty evolution. Forecast uncertaintygenerally decreases over time and as more hydrologic...
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...
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.
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...
Weighted Monte Carlo prices exotic options calibrating the probabilities of previously generated paths by a regular Monte Carlo to fit a set of option premiums. When only vanilla call and put options ...
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 the exponential Levy models and we study the conditions under which f-minimal equivalent martingale measure preserves Levy property. Then we give a general formula for optimal strategy in...
We consider the exponential Levy models and we study the conditions under which f-minimal equivalent martingale measure preserves Levy property. Then we give a general formula for optimal strategy in ...

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