Research Catalog

Title

The generalized Feller equation and related topics / S. Lehnigk.

Author

Lehnigk, Siegfried H.

Publication

Harlow, Essex, England : Longman Scientific & Technical ; New York : J. Wiley, 1993.

Items in the Library & Off-site

Holdings

Details

Description

xvi, 292 pages : illustrations; 24 cm.

Series Statement

Pitman monographs and surveys in pure and applied mathematics, 0269-3666 ; 68

Uniform Title

Pitman monographs and surveys in pure and applied mathematics ; 68.

Subjects

• Fokker-Planck equation > Numerical solutions
• Diffusion processes

Bibliography (note)

• Includes bibliographical references (p. 285-289).

Contents

• Ch. 1. The Generalized Feller Equation. 1.1. Fokker-Planck Equations and Similarity Solutions. 1.2. The Generalized Feller Equation. 1.3. A Similarity Solution. 1.4. Properties of the Boundary Points. 1.5. Related Equations. 1.6. The Lognormal Diffusion Process -- Ch. 2. The Source Solution. 2.1. A Fundamental Solution. 2.2. The Source Solution. 2.3. A Singular Integral -- Ch. 3. Initial Condition Solutions. 3.1. Poisson-Lebesgue Transform Solutions. 3.2. Poisson-Stieltjes Transform Solutions. 3.3. Integral Representation of the Source Solution. 3.4. Practical Aspects of the Source Solution -- Ch. 4. Boundary Condition Solutions. 4.1. Two Convolution Kernels. 4.2. Reduced Differential Equations. 4.3. Properties of the Convolution Kernels. 4.4. Boundary Condition Solutions -- Ch. 5. Integral Representations. 5.1. Initial and Boundary Condition Solutions. 5.2. An Extreme Value Principle. 5.3. A Uniqueness Theorem. 5.4. Bounded Solutions. 5.5. Positive Solutions -- 5.6. Examples.
• Ch. 6. Basis Functions and Series Expansions. 6.1. Sequences of Initial Condition Solutions. 6.2. Generating Functions. 6.3. Functional Estimates of the Basis Functions. 6.4. Convergence of Series Expansions. 6.5. Series Solutions. 6.6. Associated Basis Functions. 6.7. Functional Relations of the Source Solutions. 6.8. Huygens Property Solutions. 6.9. Series Expansions of Solutions -- 6.10. Examples -- Ch. 7. A Generalized Theta Function -- 7.1. Introduction. 7.2. Inequalities for [actual symbol not reproducible]. 7.3. Holomorphy of [Theta](x,t) as a Function of x. 7.4. Holomorphy of [Theta](x,t) as a Function of t. 7.5. [Theta](x,t) as a Solution of GF. 7.6. The Special Case v = 1/2 -- Ch. 8. Probability Density Functions -- 8.1. Introduction. 8.2. The Source Density. 8.3. Special Cases. 8.4. Related Densities -- Ch. 9. Parameter Estimation -- 9.1. Introduction. 9.2. Source Density Estimation. 9.3. Hyper-Gamma Density Estimation. 9.4. Lognormal Density Estimation.
• 9.5. Extreme Value Density Estimation -- Ch. 10. Characteristic Functions -- 10.1. Introduction. 10.2. The Characteristic Function for 0 < [beta] < 1. 10.3. The Characteristic Function for [beta] = 1. 10.4. The Characteristic Function for [beta] > 1.

LCCN

93000278

OCLC

• 27429783
• ocm27429783

Owning Institutions

Columbia University Libraries