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|a (DE-627)JST069352674
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|a (JST)20209273
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|a DE-627
|b ger
|c DE-627
|e rakwb
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|a eng
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|a Mijatović, Aleksandar
|e verfasserin
|4 aut
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|a Spectral Properties of Trinomial Trees
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|c 2007
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|a Text
|b txt
|2 rdacontent
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|a Computermedien
|b c
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|a Online-Ressource
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|a In this paper, we prove that the probability kernel of a random walk on a trinomial tree converges to the density of a Brownian motion with drift at the rate O(h⁴), where h is the distance between the nodes of the tree. We also show that this convergence estimate is optimal in which the density of the random walk cannot converge at a faster rate. The proof is based on an application of spectral theory to the transition density of the random walk. This yields an integral representation of the discrete probability kernel that allows us to determine the convergence rate.
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|a Copyright 2007 The Royal Society
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|a trinomial trees
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|a Brownian motion with drift
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|a convergence estimates for probability densities
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|a spectral theory
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Random walk
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|a Physical sciences
|x Physics
|x Mechanics
|x Fluid mechanics
|x Brownian motion
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
|x Stochastic processes
|x Markov processes
|x Markov chains
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Statistical physics
|x Dimensional analysis
|x Dimensionality
|x Abstract spaces
|x Topological spaces
|x Metric spaces
|x Separable spaces
|x Banach space
|x Hilbert spaces
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Spectral theory
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650 |
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4 |
|a Applied sciences
|x Computer science
|x Artificial intelligence
|x Machine learning
|x Perceptron convergence procedure
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650 |
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Linear transformations
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650 |
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4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Inner products
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650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
|x Mathematical moments
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650 |
|
4 |
|a Mathematics
|x Mathematical expressions
|x Mathematical functions
|x Mathematical transformations
|x Integral transformations
|x Laplace transformation
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650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Random walk
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650 |
|
4 |
|a Physical sciences
|x Physics
|x Mechanics
|x Fluid mechanics
|x Brownian motion
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650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
|x Stochastic processes
|x Markov processes
|x Markov chains
|
650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Statistical physics
|x Dimensional analysis
|x Dimensionality
|x Abstract spaces
|x Topological spaces
|x Metric spaces
|x Separable spaces
|x Banach space
|x Hilbert spaces
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650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Spectral theory
|
650 |
|
4 |
|a Applied sciences
|x Computer science
|x Artificial intelligence
|x Machine learning
|x Perceptron convergence procedure
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650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Linear transformations
|
650 |
|
4 |
|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Matrix theory
|x Inner products
|
650 |
|
4 |
|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
|x Mathematical moments
|
650 |
|
4 |
|a Mathematics
|x Mathematical expressions
|x Mathematical functions
|x Mathematical transformations
|x Integral transformations
|x Laplace transformation
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|a research-article
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|i Enthalten in
|t Proceedings: Mathematical, Physical and Engineering Sciences
|d The Royal Society
|g 463(2007), 2083, Seite 1681-1696
|w (DE-627)253785316
|w (DE-600)1460987-3
|x 13645021
|7 nnns
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|g volume:463
|g year:2007
|g number:2083
|g pages:1681-1696
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|u https://www.jstor.org/stable/20209273
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|d 463
|j 2007
|e 2083
|h 1681-1696
|