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Université de PoitiersTHÈSEpour o
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AbstractIn the first part of this t
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ivTABLE DES MATIÈRES3 Kendall-Cran
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8 CHAPITRE 1. INTRODUCTIONdifféren
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10 CHAPITRE 1. INTRODUCTIONdonne se
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12 CHAPITRE 1. INTRODUCTIONHamilton
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14 CHAPITRE 1. INTRODUCTIONx et ell
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16 CHAPITRE 1. INTRODUCTIONCette é
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18 CHAPITRE 1. INTRODUCTION- Exempl
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20 CHAPITRE 1. INTRODUCTION20
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22CHAPITRE 2. INTRODUCTION À L’A
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24CHAPITRE 2. INTRODUCTION À L’A
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26CHAPITRE 2. INTRODUCTION À L’A
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2. ÉQUATIONS DIFFÉRENTIELLES STOC
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2. ÉQUATIONS DIFFÉRENTIELLES STOC
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3. QUELQUES APPLICATIONS DU CALCUL
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Chapitre 3Brownian motion with resp
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for every smooth function f,is a lo
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For the solution U t of (1.1) we ge
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Remark : Recall that in the compact
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2 Local expression, evolution equat
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The last equality comes from Green
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Theorem 3.2 For every solution f(t,
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Consequently:d(df(T − t, .) X Tt
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Proof : The first remark after theo
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Remark : Hamilton gives a proof of
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Corollary 3.7 For χ(M) < 0, there
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We also have:D S,T −t dπ ˜// 0,
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Proof : By differentiation under x
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where we have used in the second eq
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[10] K. D. Elworthy and M. Yor. Con
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Chapter 4Some stochastic process wi
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We will just look at the smooth sol
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that is to say:d(Y T,it ) = − ∂
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2 Tightness, and first example on t
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proof : It is clear that F is smoot
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Proposition 2.6 Let g(t) be a famil
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v) ˜g(∞) is a metric such that (
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Then:for all ɛ > 0 , there exists
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Finally, we obtain:∂∂t | t=t 0
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