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1 Infinitesimal Calculus, Consistently and Accessibly |
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1 | (6) |
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1.1 An Accessible Axiom System for Infinitesimal Calculus: Minimal Internal Set Theory |
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1 | (3) |
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1.2 Finer Classification of the Reals: Finite vs. Limited |
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4 | (3) |
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2 Radically Elementary Probability Theory |
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7 | (12) |
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2.1 Random Variables and Stochastic Processes |
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7 | (2) |
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2.2 Integrability and Limitedness |
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9 | (4) |
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2.3 Wiener Walks and Wiener Processes |
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13 | (2) |
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2.4 Distribution of the Wiener Walk |
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15 | (1) |
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2.5 Integrability and Limited Paths of the Wiener Walk |
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16 | (3) |
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3 Radically Elementary Stochastic Integrals |
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19 | (16) |
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3.1 Martingales and I to Integrals |
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19 | (4) |
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3.2 Radically Elementary I to Processes |
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23 | (3) |
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3.3 A Basic Radically Elementary I to Formula |
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26 | (2) |
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3.4 Analytic Excursion: A Radically Elementary Treatment of Geometric I to Processes with Monotone Drift |
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28 | (5) |
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3.5 The Radically Elementary Version of Levy's Characterization of Wiener Processes |
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33 | (2) |
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4 The Radically Elementary Girsanov Theorem and the Diffusion Invariance Principle |
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35 | (10) |
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35 | (7) |
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4.2 The Radically Elementary Diffusion Invariance Principle |
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42 | (3) |
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5 Excursion to Financial Economics: A Radically Elementary Approach to the Fundamental Theorems of Asset Pricing |
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45 | (10) |
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6 Excursion to Financial Engineering: Volatility Invariance in the Black-Scholes Model |
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55 | (6) |
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7 A Radically Elementary Theory of I to Diffusions and Associated Partial Differential Equations |
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61 | (10) |
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61 | (3) |
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7.2 The Markov Property of I to Diffusions and the Feynman-Kac Formula |
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64 | (7) |
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8 Excursion to Mathematical Physics: A Radically Elementary Definition of Feynman Path Integrals |
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71 | (6) |
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9 A Radically Elementary Theory of Levy Processes |
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77 | (16) |
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9.1 Random Walks and Levy Walks |
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77 | (3) |
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9.2 Integrability of Levy Walks with Limited Increments |
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80 | (2) |
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9.3 Lindstrøm's Characterization of Levy Walks |
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82 | (4) |
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9.4 A Radically Elementary Ito-Doeblin Formula for Levy Walks with Limited-Variation Jump Part |
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86 | (4) |
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9.5 A Brief Look at Levy Finance |
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90 | (3) |
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93 | (2) |
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A Excursion to Logic: Some Remarks on the Metamathematics of Minimal Internal Set Theory |
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95 | (8) |
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A.1 An Alternative Road to Minimal Internal Set Theory |
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95 | (2) |
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A.2 A Simple Relative Consistency Proof for a Substantial Subsystem of minIST |
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97 | (4) |
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A.3 Definable Models for (Minimal) Nonstandard Analysis |
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101 | (2) |
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B Robinsonian vs. Minimal Nonstandard Analysis |
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103 | (4) |
| References |
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107 | (4) |
| Index |
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111 | |
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