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Continuous-Time Random Walks for the Numerical Solution of Stochastic Differential Equations
This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov eq...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2019.
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| Colección: | Memoirs of the American Mathematical Society Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Chapter 1. Introduction; 1.1. Motivation; 1.2. Main Results; 1.3. Relation to Other Works; 1.4. Organization of Paper; 1.5. Acknowledgements; Chapter 2. Algorithms; 2.1. Realizability Condition; 2.2. Gridded vs Gridless State Spaces; 2.3. Realizable Discretizations in 1D; 2.4. Realizable Discretizations in 2D; 2.5. Realizable Discretizations in nD; 2.6. Scaling of Approximation with System Size; 2.7. Generalization of Realizable Discretizations in nD; 2.8. Weakly Diagonally Dominant Case; Chapter 3. Examples & Applications; 3.1. Introduction
- 3.2. Cubic Oscillator in 1D with Additive Noise3.3. Asymptotic Analysis of Mean Holding Time; 3.4. Adaptive Mesh Refinement in 1D; 3.5. Log-normal Process in 1D with Multiplicative Noise; 3.6. Cox-Ingersoll-Ross Process in 1D with Multiplicative Noise; 3.7. SDEs in 2D with Additive Noise; 3.8. Adaptive Mesh Refinement in 2D; 3.9. Log-normal Process in 2D with Multiplicative Noise; 3.10. Lotka-Volterra Process in 2D with Multiplicative Noise; 3.11. Colloidal Cluster in 39D with Multiplicative Noise; Chapter 4. Analysis on Gridded State Spaces; 4.1. Assumptions
- 4.2. Stability by Stochastic Lyapunov Function4.3. Properties of Realizations; 4.4. Generator Accuracy; 4.5. Global Error Analysis; Chapter 5. Analysis on Gridless State Spaces; 5.1. A Random Walk in a Random Environment; 5.2. Generator Accuracy; 5.3. Stability by Stochastic Lyapunov Function; 5.4. Finite-Time Accuracy; 5.5. Feller Property; 5.6. Stationary Distribution Accuracy; Chapter 6. Tridiagonal Case; 6.1. Invariant Density; 6.2. Stationary Density Accuracy; 6.3. Exit Probability; 6.4. Mean First Passage Time; Chapter 7. Conclusion and Outlook; Bibliography; Back Cover