Stochastic Models for Fractional Calculus

摘要: Preface 1 Introduction 1.1 The traditional diffusion model 1.2 Fractional 2 Derivatives 2.1 Grunwald formula 2.2 More fractional derivatives 2.3 Caputo derivative 2.4 Time-fractional 3 Stable Limit Distributions 3.1 Infinitely divisible laws 3.2 characteristic functions 3.3 Semigroups 3.4 Poisson approximation 3.5 Shifted 3.6 Triangular arrays 3.7 One-sided stable limits 3.8 Two-sided 4 Continuous Time Random Walks 4.1 Regular variation 4.2 Central Theorem 4.3 time random walks 4.4 Convergence in Skorokhod space 4.5 CTRW governing equations 5 Computations R 5.1 codes for 5.2 Sample path simulations 6 Vector Diffusion 6.1 6.2 with heavy tails 6.3 of vectors 6.4 6.5 equation 6.6 Operator 6.7 regular 6.8 Generalized domains attraction 7 Applications and Extensions 7.1 LePage Series Representation 7.2 Tempered 7.3 7.4 Pearson 7.5 Classification diffusions 7.6 Spectral representations the solutions Kolmogorov 7.7 Brownian motion 7.8 fields 7.9 7.10 vector Bibliography Index