VI
Contents
Chapter 9 . Th e Loca l Limi t Theore m 5 3
Chapter 10. Th e Arcsin e La w 5 9
§10.1. Introductio n 5 9
§10.2. Statemen t o f th e Theorem s 6 0
§10.3. Th e Reflectio n Principl e 6 1
§10.4. Proo f o f th e Arcsin e La w 6 6
§10.5. Proo f o f th e La w o f Return s t o th e Origi n 7 3
Chapter 11 . Th e Stron g La w o f Larg e Number s 7 7
§11.1. Almos t Sur e Events , Independen t Event s 7 8
§11.2. Borel' s Stron g La w o f Larg e Number s 8 2
§11.3. Rando m Sequence s Takin g Severa l Value s 8 5
§11.4. Norma l Number s 8 6
§11.5. Th e Borel-Cantell i Lemma s 8 9
Chapter 12. Th e La w o f th e Iterate d Logarith m 9 7
§12.1. Introductio n 9 7
§12.2. HausdorfF s Estimat e 9 9
§12.3. Hard y an d Littlewood' s Estimat e 100
§12.4. Khinchin' s La w o f the Iterate d Logarith m 100
Chapter 13. Recurrenc e o f Rando m Walk s 109
§13.1. Introductio n an d Definition s 109
§13.2. Neares t Neighbo r Rando m Walk s o n Z 111
§13.3. Genera l Result s abou t Rando m Walk s 112
§13.4. Recurrenc e o f Rando m Walk s o n Z N 121
Chapter 14. Epilogu e 13
§14.1. A Fe w Mor e Genera l Result s 131
§14.2. Closin g Remark s 135
Biographies 137
Bibliography 147
Index 149
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