Stochastic processes and orthogonal polynomials

By Wim Schoutens. 2000

410 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a99304b00d503bebebad33704d640531ccc61b1f

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In Statistics and Probability

Citations in the corpus

The Meixner process : theory and applications in finance (2002, background): “It was introduced in [27] (see also [28]) and originates from the theory of orthogonal polynomials and was proposed to serve as a model of financial data in [15].”
Testing Distributional Assumptions: A GMM Approach (2007, background): “In this section, we will follow Johnson, Kotz and Balakrishnan (1994), Wong (1964), and Schoutens (2000) to present the Pearson’s class of distributions and their connections with (2.”
Dam rain and cumulative gain (2007, background): “In particular, by setting h = mt and z = γt in equation (12), we are able to deduce that for each value of n the process {L (mt−n) n (γt)} is a martingale (cf. Schoutens 2000).”
Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos (2002, background): “1 (following [28]), classifies the hypergeometric orthogonal polynomials and indicates the limit relations between them.”
Inverse Problems in Heat Transfer (2009, methodology): “In more recent work [30, 32] uses the generalized Askey system of orthogonal polynomials [46] as trial bases for the probability space.”
Density Approximations for Multivariate Affine Jump-Diffusion Processes (2011, methodology): “That is, the support of the density approximation agrees with the support of the true, unknown transition density as in Hurn et al. (2008) and Schoutens (2000); (v) produces density approximations that integrate to unity by construction, hence are much more amenable to applications that demand the…”
Uncertainty quantification in chemical systems (2009, methodology): “This construction was extended to a generalized polynomial chaos (GPC) representation [25], employing a range of orthogonal polynomials in the Askey scheme [26, 27], coupled with associated RV bases.”
Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs* (2011, background): “We focus on Gaussian and on uniform measures, where ‘polynomial chaos’ representations use Hermite and Legendre polynomials, respectively (other probability measures give rise to other polynomial systems: see, e.g., Schoutens (2000) and Xiu and Karniadakis (2002b)).”
Stochastic Analysis of Multiconductor Cables and Interconnects (2011, background): “For a comprehensive and formal discussion of PC theory, the reader is referred to [2], [3], and [ 12 ] and references therein.”
Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs (2010, methodology): “The spectral approach is based on the so-called Wiener/generalized polynomial chaos expansion introduced in [22] (see also [9] and [15]).”
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems (2008, background): “(25) Polynomial chaos (PC) expansions have been generalized to broader classes of orthogonal polynomials in the Askey scheme, each family resulting from a different choice of distribution for the ξi [10, 57].”
Static Hedging of Asian Options under Lévy Models (2005, methodology): “The Meixner process was introduced in [32] (see also [33]) and later on it was suggested to serve for fitting stock returns in [22].”
Polynomials of Meixner's type in infinite dimensions-Jacobi fields and orthogonality measures (2002, methodology): “Though the one-dimensional polynomials of Meiner’s type were used in this work in order to carry out the orthogonalization procedure of the Teugels martingales (which, in turn, are the centered power jump processes related to the original process), infinite-dimensional polynomials corresponding to t”