Stochastic Processes and Orthogonal Polynomials

Inhaltsverzeichnis

• 1 The Askey Scheme of Orthogonal Polynomials.
• 2.1 Markov Processes.
• 3 Birth and Death Processes, Random Walks, and Orthogonal Polynomials.
• 4 Sheffer Systems.
• 5 Orthogonal Polynomials in Stochastic Integration Theory.
• Stein Approximation and Orthogonal Polynomials.
• Conclusion.
• A Distributions.
• B Tables of Classical Orthogonal Polynomials.
• B.1 Hermite Polynomials and the Normal Distribution.
• B.2 Scaled Hermite Polynomials and the Standard Normal Distribution.
• B.3 Hermite Polynomials with Parameter and the Normal Distribution.
• B.4 Charlier Polynomials and the Poisson Distribution.
• B.5 Laguerre Polynomials and the Gamma Distribution.
• B.6 Meixner Polynomials and the Pascal Distribution.
• B.7 Krawtchouk Polynomials and the Binomial Distribution.
• B.8 Jacobi Polynomials and the Beta Kernel.
• B.9 Hahn Polynomials and the Hypergeometric Distribution.
• C Table of Duality Relations Between Classical Orthogonal Polynomials.
• D Tables of Sheffer Systems.
• D.1 Sheffer Polynomials and Their Generating Functions.
• D.2 Sheffer Polynomials and Their Associated Distributions.
• D.3 Martingale Relations with Sheffer Polynomials.
• E Tables of Limit Relations Between Orthogonal Polynomials in the Askey Scheme.
• References.