THÃSE KolÃ©hÃ¨ Abdoulaye COULIBALY-PASQUIER

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34CHAPITRE 2. INTRODUCTION À L’ANALYSE STOCHASTIQUE SUR LESVARIÉTÉS34
Chapitre 3Brownian motion with respect totime-changing Riemannian metrics,applications to Ricci flow3535
Page 1: Université de PoitiersTHÈSEpour o
Page 4 and 5: AbstractIn the first part of this t
Page 6 and 7: ivTABLE DES MATIÈRES3 Kendall-Cran
Page 8 and 9: 8 CHAPITRE 1. INTRODUCTIONdifféren
Page 10 and 11: 10 CHAPITRE 1. INTRODUCTIONdonne se
Page 12 and 13: 12 CHAPITRE 1. INTRODUCTIONHamilton
Page 14 and 15: 14 CHAPITRE 1. INTRODUCTIONx et ell
Page 16 and 17: 16 CHAPITRE 1. INTRODUCTIONCette é
Page 18 and 19: 18 CHAPITRE 1. INTRODUCTION- Exempl
Page 20 and 21: 20 CHAPITRE 1. INTRODUCTION20
Page 22 and 23: 22CHAPITRE 2. INTRODUCTION À L’A
Page 24 and 25: 24CHAPITRE 2. INTRODUCTION À L’A
Page 26: 26CHAPITRE 2. INTRODUCTION À L’A
Page 29 and 30: 2. ÉQUATIONS DIFFÉRENTIELLES STOC
Page 31 and 32: 2. ÉQUATIONS DIFFÉRENTIELLES STOC
Page 33: 3. QUELQUES APPLICATIONS DU CALCUL
Page 37 and 38: for every smooth function f,is a lo
Page 39 and 40: For the solution U t of (1.1) we ge
Page 41 and 42: Remark : Recall that in the compact
Page 43 and 44: 2 Local expression, evolution equat
Page 45 and 46: The last equality comes from Green
Page 47 and 48: Theorem 3.2 For every solution f(t,
Page 49 and 50: Consequently:d(df(T − t, .) X Tt
Page 51 and 52: Proof : The first remark after theo
Page 53 and 54: Remark : Hamilton gives a proof of
Page 55 and 56: Corollary 3.7 For χ(M) < 0, there
Page 57 and 58: We also have:D S,T −t dπ ˜// 0,
Page 59 and 60: Proof : By differentiation under x
Page 61 and 62: where we have used in the second eq
Page 63 and 64: [10] K. D. Elworthy and M. Yor. Con
Page 65 and 66: Chapter 4Some stochastic process wi
Page 67 and 68: We will just look at the smooth sol
Page 69 and 70: that is to say:d(Y T,it ) = − ∂
Page 71 and 72: 2 Tightness, and first example on t
Page 73 and 74: proof : It is clear that F is smoot
Page 75 and 76: Proposition 2.6 Let g(t) be a famil
Page 77 and 78: v) ˜g(∞) is a metric such that (
Page 79 and 80: Then:for all ɛ > 0 , there exists
Page 81 and 82: Finally, we obtain:∂∂t | t=t 0
Page 83 and 84: where Ut 3 is the horizontal lift o
Page 85 and 86:
√πWe can choose ɛ, ɛ 2 such th
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We will now show that the coupling
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HenceWe get:√√ n∑1 − ɛI t
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By uniqueness in law of such proces
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Chapter 5Horizontal diffusion in pa
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2 M. ARNAUDON, A. K. COULIBALY, AND
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Page 105 and 106:
10 M. ARNAUDON, A. K. COULIBALY, AN
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Chapter 6Compléments de calculs113
Page 115 and 116:
d’avoir une famille de connexion,
Page 117 and 118:
Dans le calcul de ligne 8 à ligne
Page 119 and 120:
On utilise le fait que W (.) t est
Page 121 and 122:
Chapter 7Appendix121121
Page 123 and 124:
774 M. Arnaudon et al. / C. R. Acad
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Bibliography[ABT02]Marc Arnaudon, R
Page 131 and 132:
BIBLIOGRAPHY 131[DeT83][Dri92]Denni
Page 133 and 134:
BIBLIOGRAPHY 133[Jos84][Jos05][JS03
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THÃSE KolÃ©hÃ¨ Abdoulaye COULIBALY-PASQUIER

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THÃSE KolÃ©hÃ¨ Abdoulaye COULIBALY-PASQUIER