The book serves as a synergistic link between the development of mathematical models and the emergence of stochastic (Monte Carlo) methods applied for the simulation of current transport in electronic devices. Regarding the models, the historical evolution path, beginning from the classical charge carrier transport models for microelectronics to current quantum-based nanoelectronics, is explicatively followed. Accordingly, the solution methods are elucidated from the early phenomenological single particle algorithms applicable for stationary homogeneous physical conditions up to the complex algorithms required for quantum transport, based on particle generation and annihilation. The book fills the gap between monographs focusing on the development of the theory and the physical aspects of models, their application, and their solution methods and monographs dealing with the purely theoretical approaches for finding stochastic solutions of Fredholm integral equations.

Part I Aspets of Electron Transport Modeling: 1. Concepts of Device Modeling.- 2. The Semiconductor Model: Fundamentals.- 3. Transport Theories in Phase Space.- 4. Monte Carlo Computing.- Part II Stochastic Algorithms for Boltzmann Transport: 5. Homogeneous Transport: Empirical Approach.- 6. Homogeneous Transport: Stochastic Approach.- 7. Small Signal Analysis.- 8. Inhomogeneous Stationary Transport.- 9. General Transport: Self-Consistent Mixed Problem.- 10. Event Biasing.- Part III Stochastic Algorithms for Quantum Transport: 11. Wigner Function Modeling.- 12. Evolution in a Quantum Wire.- 13. Hierarchy of Kinetic Models.- 14. Stationary Quantum Particle Attributes.- 15. Transient Quantum Particle Attributes.