1. Introduction
  References
2. Basic Concepts of Cascade Theory
  2.1 The General Scheme of the Cascade Process
  2.2 Mathematical Expectation of a Measurand
  2.3 Multiparticle Densities
  2.4 Fluctuations of a Functional from a Random Measure
  2.5 Characteristic and Generating Functionals
  2.6 Interrelations Between Multiparticle Densities
  References
3. Forward (Basic) Equation for CP
  3.1 The Generating Functional
  3.2 Equations for GF
  3.3 One-Particle Direct Equations
  3.4 Multiparticle Direct Equations
  3.5 Green’s Function
  3.6 The Diagrammatic Representation
  3.7 Dynamics of Correlation Forms
  References
4. Backward (Adjoint) Equation
  4.1 Processes with a Single-Particle Initial State
  4.2 Backward Equations for GFs and Multiparticle Densities
  4.3 Multiparticle Importance Functions
  4.4 Adjoint Equations and Adjoint Functions
  4.5 The Perturbation Theory
  4.6 Fluctuations and Correlations in Linear Functionals
  4.7 Equations for Moments and Distribution of a Linear Functional
  4.8 Fluctuations in an Arbitrary Additive Functional
  References
5. Electrons and Photons
  5.1 Photon Birth (Classical Sketch)
  5.2 Electromagnetic Field Operators
  5.3 Bremsstrahlung (Quantum Sketch)
  5.4 Compton Scattering
  5.5 Photo Absorption and Pair Production
  5.6 Continuous Energy Loss Model
  5.7 Electron Multiple Scattering
    5.7.1 Energy Losses and Straggling (After Bohr)
    5.7.2 Fluctuations in Energy Losses (After Landau)
    5.7.3 The Linked Generalized Limit Theorem
    5.7.4 The Angular Distribution (After Fermi)
  5.8 Electron-Photon Cascades
  5.9 Cascade Equations in Mellin’s Transforms
  References
6. Analytical Theory
  6.1 Basic Equation of EPC Theory
  6.2 Cascade Curves
    6.2.1 Electron Cascade Curve (From Primary Electron)
    6.2.2 Electron Cascade Curve (From Primary Photon)
  6.3 Degradation Spectrum Problem
    6.3.1 Electron Energy Degradation Spectrum
    6.3.2 Photon Energy Degradation Spectrum
    6.3.3 On Accuracy of Degradation Spectra
  6.4 Longitudinal Moment Method
    6.4.1 Cascade Curve Phenomenology
    6.4.2 Cascade Curves’ Reconstruction
  6.5 Including Electron Scattering
  6.6 Beyond Small-Angle Approximation
  6.7 Nishimura-Kamata Theory
  References
7. SBCE Method
  7.1 Lagrange Polynomial Interpolation
  7.2 Straight-Ahead Equation System
  7.3 Solving Straight-Ahead System
  7.4 Integral Terms in SBCE for Statistical Moments
  7.5 Some Details in Bremsstrahlung Term
  7.6 The SBCE Results Review
    7.6.1 The Total Electron Trace Length in an Infinite Medium
    7.6.2 Cascade Curves
    7.6.3 Particle Number Fluctuations
    7.6.4 Cherenkov Radiation in Atmosphere
    7.6.5 LPM Effect
  7.7 Small-Angle Approximation
  7.8 Angular Electron Distributions
  7.9 Lateral Electron Distribution
  References
8. Statistical Fluctuations in EPC
  8.1 Fluctuations in Electron Number
  8.2 The Electrons Total Trace Length
  8.3 Fluctuations of Electron Path in a Layer
  8.4 On the First Free Path in EPC Fluctuations
  8.5 Random Moments Method (Longitudinal Development)
    8.5.1 Fluctuations in Cascade Curves
    8.5.2 Correlations in Cascade Curves
    8.5.3 Moment Covariance Matrix Equation
    8.5.4 Some Parameter Estimations
    8.5.5 On the Detector Reading Probability Distribution
  8.6 Transverse Randomness
  References
9. Cascades in Calorimeters
  9.1 The Transition Effects
  9.2 The Perturbation Theory Formulas
  9.3 Adjoint Functions for Transition Effect
  9.4 Flux Perturbation by Boundaries
  9.5 Belenky’s Comment of the Transition Effect
  9.6 Transition Effect at Shower Maximum
  9.7 Total Particle Flux at a Boundary
  9.8 Scintillation and Ionization Chambers
  9.9 Transition Effect in Electromagnetic Calorimetry
  9.10 Determination of the π-Meson Beam Composition
  References
10. Monte Carlo Modeling
  10.1 Introduction
  10.2 Random Numbers
  10.3 Non-branching Trajectory in a Homogeneous Medium
  10.4 The Measured Characteristics of Particle Transport
  10.5 Non-analog Simulation of Detector Response
  10.6 Non-analog Simulation of Trajectories
  10.7 The Variance of Estimators
  10.8 Examples of Weight MC Modifications
  10.9 Weighting Estimation of Correlations in Branching Processes
    10.9.1 Equations for the Distribution Function and Its Moments
    10.9.2 The First Moment Modified Estimation
    10.9.3 Some Examples
    10.9.4 The Modified Estimation of the Second Moment
  10.10 AEGIS Code
  References
11. Stochastic Phenomenology of EAS
  11.1 EAS Structure
  11.2 Multiple Process Models
  11.3 Parametric Sensitivity Analysis
  11.4 Functional Sensitivity Analysis
  11.5 Solving Equations for Second Moments
  11.6 EAS Covariance Matrix
  11.7 Inelasticity and Multiplicity Fluctuations
  11.8 Two-Component Model of Fluctuations
  References
12. Cherenkov Radiation of EPC
  12.1 Radiation in a Homogeneous Medium (B-Approximation)
  12.2 Cherenkov Radiation in Water (Monte Carlo)
  12.3 Cherenkov Radiation in Atmosphere
  12.4 ALTAI Code
    12.4.1 Electromagnetic Cascade
    12.4.2 Emission of Cherenkov Light
    12.4.3 Hadron-Nuclei Cascade
    12.4.4 Nucleus-Nucleus Interactions
    12.4.5 Comparison with Other Codes and Data
  12.5 Semianalytical Monte Carlo Method
    12.5.1 The SAMC Philosophy
    12.5.2 Equations for Equivalent Sources
    12.5.3 Sampling From the Equivalent Source
    12.5.4 Primary-Energy Correction
    12.5.5 The SAMC Errors and CTMC Estimation
  12.6 The Lateral Light Distribution
  12.7 Fluctuations in the Cherenkov Light Amplitude
  12.8 Time Structure of the Cherenkov Signal
  12.9 Cherenkov Image of EPC
  References
13. Relativistic EPC in Intergalactic Medium
  13.1 Introduction
  13.2 The Ivanenko-Sizov Theory
  13.3 EPC From Monoenergetic Source
  13.4 EPC in Monochromatic Photon Field
  13.5 Variational Analysis
  13.6 EPC in Magnetic Fields
  References
14. Cascade Ages, Similarity, Universality, and All That
  14.1 Longitudinal Parameterizations and Uncertainties
  14.2 EAS with Respect to the Shower Age
  14.3 Lateral Distribution Fitting
  14.4 The TAP-LAP Analysis
  14.5 Space-Time Similarity Relations in Inclined Air Showers
  References
Appendix A: Method of Integral Transformations
Appendix B: An Excerpt From Ivanenko-Roganova Book
Appendix C: A Few Images From Prof. Ivanenko Scientific Group Archiv
Index
Author Index