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Martingale Central Limit Theorem and Nonuniformly Hyperbolic Systems
hyperbolic systems nonuniformly
2014/12/8
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...
Critical Gaussian Multiplicative Chaos: Convergence of the Derivative Martingale
Critical Gaussian Multiplicative Chaos Convergence of the Derivative Martingale Probability
2012/6/29
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...
Martingale transform and Levy Processes on Lie Groups
Martingale transform Levy Processes Lie Groups Probability
2012/6/29
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...
Galton-Watson trees with vanishing martingale limit
Conditioning principle large deviations micro-canonical distribution sharp thresholds branching entropic repulsion
2012/4/16
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...
Martingale Couplings and Bounds on the Tails of Probability Distributions
Martingale Couplings and Bounds Probability Distributions Statistics Theory
2011/8/30
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...
Finitely additive equivalent martingale measures
Arbitrage de Finetti’s coherence principle equivalent martin-gale measure
2011/1/21
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.
Parametrix techniques and martingale problem for some degenerate Kolmogorov's equations
Parametrix techniques martingale problem degenerate Kolmogorov's equations
2010/11/15
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...
Construction of the minimal entropy martingale measure in finite probability market models
Relative entropy Minimal entropy martingale measure
2010/9/13
The principle of minimization of relative entropy is used to construct a minimal entropy martingale measure for a finite probability/multiperiod market model.
Martingale problems on Banach spaces -- Existence, uniqueness and the Markov property
Martingale solution strong Markov property stochastic partial differential equation
2010/12/6
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 ...
Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
Non-equilibrium Markovian Process Fluctuation-Dissipation Theorems Fluctuation Relations Martingale
2010/12/15
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 ...
Martingale representation for Poisson processes with applications to minimal variance hedging
Poisson process martingalerep resentation Clark-Ocone formula derivative operator Kunita-Watanabe decomposition Malliavin calculus independent random measure minimal variance hedge
2010/4/27
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 $\lambda$ ...
The martingale approach for credit-risky exchange option pricing
Exchange option Girsanov’s theorem
2010/9/10
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...
Martingale Inequalities in Exponential Orlicz Spaces
Orlicz space BDG-inequalities exponential model
2010/1/22
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 ...
Valuation of real options using the minimal entropy martingale measure
Real Options Analysis Minimal Entropy Martingale Measure
2010/9/14
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...
A Note on the Martingale Inequality
Bounded Martingale Deviation bound Hoeffding inequality Martingale inequality
2008/7/3
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...