- Page 1: Université de PoitiersTHÈSEpour o
- Page 5 and 6: Table des matièresRésumé . . . .
- Page 7 and 8: Chapitre 1IntroductionLa première
- Page 9 and 10: 9L’équation d’évolution, donn
- Page 11 and 12: 11Définition 0.1 Soit g(t) t∈[0,
- Page 13 and 14: 13Hamilton a démontré que ce flot
- Page 15 and 16: 15Si T < T c , x 0 un point de M et
- Page 17 and 18: 17superflu du flot stochastique, vo
- Page 19 and 20: 19On retrouve ainsi, avec des méth
- Page 21 and 22: Chapitre 2Introduction à l’analy
- Page 23 and 24: 1. LA GÉOMÉTRIE D’ORDRE DEUX, C
- Page 25 and 26: 1. LA GÉOMÉTRIE D’ORDRE DEUX, C
- Page 28 and 29: 28CHAPITRE 2. INTRODUCTION À L’A
- Page 30 and 31: 30CHAPITRE 2. INTRODUCTION À L’A
- Page 32 and 33: 32CHAPITRE 2. INTRODUCTION À L’A
- Page 34 and 35: 34CHAPITRE 2. INTRODUCTION À L’A
- Page 36 and 37: Brownian motion with respect to tim
- Page 38 and 39: We write ∂ 1 g(t, x) for ∂ s g(
- Page 40 and 41: Remark : Isometry of U t forces A t
- Page 42 and 43: We have a similar result for the hy
- Page 44 and 45: Hence:dX j t = σ i,j (X t )dB i
- Page 46 and 47: For the forward Ricci flow (2.2), w
- Page 48 and 49: We shall make separate computations
- Page 50 and 51: Remark :For the forward Ricci flow,
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Proof : Take x ∈ M such that ‖
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Recall that for the surface:consequ
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Define the Itô stochastic equation
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Proposition 4.2 For all v ∈ T x M
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Proof :Recall that by the same cons
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Remark : We could choose E i such t
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[23] Anton Thalmaier and Feng-Yu Wa
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Some stochastic process without bir
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Remark : Sometimes we will use a pr
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and in the Itô’s sense:HencedX T
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Also by the above remark Y ɛ0 is t
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Proposition 2.5 Let ϕ = (ɛ k ) k
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Now consider the solution of:i.e. t
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proof :Let f ∈ C ∞ (M) and s <
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Also, for all ɛ > 0, there exists
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for some constant cst 1 , and we us
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Let f ∈ C ∞ (M) then we have:fo
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It follows that:(dρ −∞ (Z 1 t
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where G(0) = G(r) = 1. We have:‖
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Let f 1 ...f m ∈ B b (M) (bounded
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[10] L. C. Evans and J. Spruck. Mot
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HORIZONTAL DIFFUSION IN C 1 PATH SP
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HORIZONTAL DIFFUSION IN PATH SPACE
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HORIZONTAL DIFFUSION IN PATH SPACE
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HORIZONTAL DIFFUSION IN PATH SPACE
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HORIZONTAL DIFFUSION IN PATH SPACE
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HORIZONTAL DIFFUSION IN PATH SPACE
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HORIZONTAL DIFFUSION IN PATH SPACE
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HORIZONTAL DIFFUSION IN PATH SPACE
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HORIZONTAL DIFFUSION IN PATH SPACE
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1 Compléments de calculs sur le ch
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2 Compléments de calculs sur le ch
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i.e.( d dt P t(.)) = −Γ(P t (.))
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où ∇ ′ désigne le lift comple
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C. R. Acad. Sci. Paris, Ser. I 346
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M. Arnaudon et al. / C. R. Acad. Sc
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M. Arnaudon et al. / C. R. Acad. Sc
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128
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130 BIBLIOGRAPHY[AT03]Marc Arnaudon
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132 BIBLIOGRAPHY[ES95] Lawrence C.
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134 BIBLIOGRAPHY[RY99] Daniel Revuz
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TitreÉtude d’équations d’évo