Results 1  10
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14
Maximum A Posteriori Estimation for Multivariate Gaussian Mixture Observations of Markov Chains
 IEEE Transactions on Speech and Audio Processing
, 1994
"... In this paper a framework for maximum a posteriori (MAP) estimation of hidden Markov models (HMM) is presented. Three key issues of MAP estimation, namely the choice of prior distribution family, the specification of the parameters of prior densities and the evaluation of the MAP estimates, are addr ..."
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Cited by 491 (39 self)
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In this paper a framework for maximum a posteriori (MAP) estimation of hidden Markov models (HMM) is presented. Three key issues of MAP estimation, namely the choice of prior distribution family, the specification of the parameters of prior densities and the evaluation of the MAP estimates, are addressed. Using HMMs with Gaussian mixture state observation densities as an example, it is assumed that the prior densities for the HMM parameters can be adequately represented as a product of Dirichlet and normalWishart densities. The classical maximum likelihood estimation algorithms, namely the forwardbackward algorithm and the segmental kmeans algorithm, are expanded and MAP estimation formulas are developed. Prior density estimation issues are discussed for two classes of applications: parameter smoothing and model adaptation, and some experimental results are given illustrating the practical interest of this approach. Because of its adaptive nature, Bayesian learning is shown to serve as a unified approach for a wide range of speech recognition applications
Random matrices and random permutations
 Internat. Math. Res. Notices
, 2000
"... We prove the conjecture of Baik, Deift, and Johansson which says that with respect to the Plancherel measure on the set of partitions λ of n, the rows λ1,λ2,λ3,... of λ behave, suitably scaled, like the 1st, 2nd, 3rd, and so on eigenvalues of a Gaussian random Hermitian matrix as n → ∞. Our proof is ..."
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Cited by 62 (7 self)
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We prove the conjecture of Baik, Deift, and Johansson which says that with respect to the Plancherel measure on the set of partitions λ of n, the rows λ1,λ2,λ3,... of λ behave, suitably scaled, like the 1st, 2nd, 3rd, and so on eigenvalues of a Gaussian random Hermitian matrix as n → ∞. Our proof is based on an interplay between maps on surfaces and ramified coverings of the sphere. We also establish a connection of this problem with intersection theory on the moduli spaces of curves. 1
Central limit theorem for linear eigenvalue statistics of random matrices with . . .
, 2009
"... We consider n × n real symmetric and Hermitian Wigner random matrices n −1/2 W with independent (modulo symmetry condition) entries and the (null) sample covariance matrices n −1 X ∗ X with independent entries of m × n matrix X. Assuming first that the 4th cumulant (excess) κ4 of entries of W and X ..."
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Cited by 9 (0 self)
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We consider n × n real symmetric and Hermitian Wigner random matrices n −1/2 W with independent (modulo symmetry condition) entries and the (null) sample covariance matrices n −1 X ∗ X with independent entries of m × n matrix X. Assuming first that the 4th cumulant (excess) κ4 of entries of W and X is zero and that their 4th moments satisfy a Lindeberg type condition, we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem (CLT) as n → ∞, m → ∞, m/n → c ∈ [0, ∞) with the same variance as for Gaussian matrices if the test functions of statistics are smooth enough (essentially of the class C 5). This is done by using a simple “interpolation trick ” from the known results for the Gaussian matrices and the integration by parts, presented in the form of certain differentiation formulas. Then, by using a more elaborated version of the techniques, we prove the CLT in the case of nonzero excess of entries again for essentially C 5 test function. Here the variance of statistics contains an additional term proportional to κ4. The proofs of all limit theorems follow essentially the same scheme.
Pricing the American put option: a detailed convergence analysis for binomial models
 Journal of Economic Dynamics and Control
, 1998
"... Leisen and Reimer (1996) suggested to consider the order of convergence as a measure of convergence speed for European call options. In this paper we study in a first step the problem of determining the order of convergence in pricing American put options for several approaches in the literature. We ..."
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Cited by 5 (1 self)
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Leisen and Reimer (1996) suggested to consider the order of convergence as a measure of convergence speed for European call options. In this paper we study in a first step the problem of determining the order of convergence in pricing American put options for several approaches in the literature. We will then examine in detail extrapolation and the Control Variate technique for improving convergence and will explain their pitfalls. Since the investigation reveals the need for smooth converging models in order to get smaller initial errors, such a model is constructed. The different approaches are then tested: simulations exhibit up to 100 times smaller initial errors. � 1998 Published by Elsevier
Lyapunov exponents in continuum BernoulliAnderson models
"... We study onedimensional, continuum BernoulliAnderson models with general singlesite potentials and prove positivity of the Lyapunov exponent away from a discrete set of critical energies. The proof is based on Furstenberg's Theorem. The set of critical energies is described explicitly in term ..."
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Cited by 4 (3 self)
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We study onedimensional, continuum BernoulliAnderson models with general singlesite potentials and prove positivity of the Lyapunov exponent away from a discrete set of critical energies. The proof is based on Furstenberg's Theorem. The set of critical energies is described explicitly in terms of the transmission and reflection coefficients for scattering at the singlesite potential. In examples we discuss the asymptotic behavior of generalized eigenfunctions at critical energies.
Decoherence Produces Coherent States: An Explicit Proof For Harmonic Chains
, 1994
"... We study the behavior of infinite systems of coupled harmonic oscillators as the time t ! 1, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This shows that generalized coherent states tend to be produc ..."
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Cited by 3 (0 self)
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We study the behavior of infinite systems of coupled harmonic oscillators as the time t ! 1, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This shows that generalized coherent states tend to be produced naturally. A sufficient condition for this to happen is shown to be that the spectral function is analytic and nonlinear. For a chain of coupled oscillators, the nonlinearity requirement means that waves must be dispersive, so that localized wavepackets become suppressed. Virtually all harmonic heatbath models in the literature satisfy this constraint, and we have good reason to believe that coherent states and their generalizations are not merely a useful analytical tool, but that nature is indeed full of them. Standard proofs of the CLT rely heavily on the fact that probability densities are nonnegative. Although the CLT is generally not applicable if the densities are allowed to take negative values, we show that a CLT does indeed hold for a special class of such functions. We find that, intriguingly, nature has arranged things so that all Wigner functions belong to this class. PACS Codes: 5.30.d, 5.30.ch, 2.50.+s, 3.65.w y Published in Phys. Rev. E, 50, 2538 (1994) 1 I.
Soliton Turbulence as a Thermodynamic Limit of Stochastic Soliton Lattices
, 2000
"... Abstract We use recently introduced notion of stochastic soliton lattice for quantitative description of soliton turbulence. We consider the stochastic soliton lattice on a special bandgap scaling of the spectral surface of genus N so that the integrated density of states remains finite as N → ∞ ( ..."
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Cited by 2 (2 self)
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Abstract We use recently introduced notion of stochastic soliton lattice for quantitative description of soliton turbulence. We consider the stochastic soliton lattice on a special bandgap scaling of the spectral surface of genus N so that the integrated density of states remains finite as N → ∞ (thermodynamic type limit). We prove existence of the limiting stationary ergodic process and associate it with the soliton turbulence. The phase space of the soliton turbulence is a onedimensional space with the random Poisson measure. The zero density limit of the soliton turbulence coincides with the Frish Lloyd potential of the quantum theory of disordered systems. 1
Artificial neural networks as approximators of stochastic processes
 Neural Networks
, 1999
"... Artificial (or biological) Neural Networks must be able to form by learning internal memory of the environment to determine decisions and subsequent actions to stimuli. By assuming that environment is essentially stochastic it follows that the mathematical framework for learning information from env ..."
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Artificial (or biological) Neural Networks must be able to form by learning internal memory of the environment to determine decisions and subsequent actions to stimuli. By assuming that environment is essentially stochastic it follows that the mathematical framework for learning information from environment is the theory of stochastic processes approximation. The aim of this paper is to show that classes of neural networks capable of approximating stochastic processes exist. 1
Stochastic Soliton Lattices by
, 1998
"... Crossroads ’ in honour of the 60th birthday of S.P. Novikov, ..."
Kronecker’s Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus
, 2002
"... For the free models of statistical mechanics on torus, exact asymptotic expansions of the free energy, the internal energy and the specific heat in the vicinity of the critical point are found. It is shown that there is direct relation between the terms of the expansion and the Kronecker’s double se ..."
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For the free models of statistical mechanics on torus, exact asymptotic expansions of the free energy, the internal energy and the specific heat in the vicinity of the critical point are found. It is shown that there is direct relation between the terms of the expansion and the Kronecker’s double series. The latter can be expressed in terms of the elliptic θfunctions in all orders of the asymptotic expansion.