| Introduction | p. v |
| Keywords, chapter by chapter | p. vii |
| The Gaussian space of BM | p. 1 |
| A realization of Brownian bridges | p. 2 |
| The filtration of Brownian bridges | p. 3 |
| An ergodic property | p. 5 |
| A relationship with space-time harmonic functions | p. 7 |
| Brownian motion and Hardy's inequality in L[superscript 2] | p. 11 |
| Fourier transform and Brownian motion | p. 14 |
| The laws of some quadratic functionals of BM | p. 17 |
| Levy's area formula and some variants | p. 18 |
| Some identities in law and an explanation of them via Fubini's theorem | p. 24 |
| The laws of squares of Bessel processes | p. 27 |
| Squares of Bessel processes and Ray-Knight theorems for Brownian local times | p. 31 |
| The basic Ray-Knight theorems | p. 32 |
| The Levy-Khintchine representation of Q[subscript x superscript delta] | p. 34 |
| An extension of the Ray-Knight theorems | p. 37 |
| The law of Brownian local times taken at an independent exponential time | p. 39 |
| Squares of Bessel processes and squares of Bessel bridges | p. 41 |
| Generalized meanders and squares of Bessel processes | p. 47 |
| Generalized meanders and Bessel bridges | p. 51 |
| An explanation and some extensions of the Ciesielski-Taylor identities | p. 57 |
| A pathwise explanation of (4.1) for [delta] = 1 | p. 58 |
| A reduction of (4.1) to an identity in law between two Brownian quadratic functionals | p. 59 |
| Some extensions of the Ciesielski-Taylor identities | p. 60 |
| On a computation of Foldes-Revesz | p. 64 |
| On the winding number of planar BM | p. 67 |
| Preliminaries | p. 67 |
| Explicit computation of the winding number of planar Brownian motion | p. 70 |
| On some exponential functionals of Brownian motion and the problem of Asian options | p. 79 |
| The integral moments of A[subscript t superscript (v)] | p. 81 |
| A study in a general Markovian set-up | p. 84 |
| The case of Levy processes | p. 87 |
| Application to Brownian motion | p. 88 |
| A discussion of some identities | p. 96 |
| Some asymptotic laws for multidimensional BM | p. 101 |
| Asymptotic windings of planar BM around n points | p. 102 |
| Windings of BM in IR[superscript 3] | p. 105 |
| Windings of independent planar BM's around each other | p. 107 |
| A unified picture of windings | p. 107 |
| The asymptotic distribution of the self-linking number of BM in IR[superscript 3] | p. 109 |
| Some extensions of Paul Levy's arc sine law for BM | p. 115 |
| Some notation | p. 116 |
| A list of results | p. 117 |
| A discussion of methods - Some proofs | p. 120 |
| An excursion theory approach to F. Petit's results | p. 125 |
| A stochastic calculus approach to F. Petit's results | p. 133 |
| Further results about reflecting Brownian motion perturbed by its local time at 0 | p. 137 |
| A Ray-Knight theorem for the local times of X, up to [tau subscript s superscript mu], and some consequences | p. 137 |
| Proof of the Ray-Knight theorem for the local times of X | p. 140 |
| Generalisation of a computation of F. Knight | p. 144 |
| Towards a pathwise decomposition of (X[subscript u]; u [less than or equal] [tau subscript s superscript mu]) | p. 149 |
| On principal values of Brownian and Bessel local times | p. 153 |
| Yamada's formulae | p. 154 |
| A construction of stable processes, involving principal values of Brownian local times | p. 157 |
| Distributions of principal values of Brownian local times, taken at an independent exponential time | p. 158 |
| Bertoin's excursion theory for BES(d), 0 < d < 1 | p. 159 |
| Probabilistic representations of the Riemann zeta function and some generalisations related to Bessel processes | p. 165 |
| The Riemann zeta function and the 3-dimensional Bessel process | p. 165 |
| The right hand side of (11.4), and the agreement formulae between laws of Bessel processes and Bessel bridges | p. 169 |
| A discussion of the identity (11.8) | p. 171 |
| A strengthening of Knight's identity, and its relation to the Riemann zeta function | p. 175 |
| Another probabilistic representation of the Riemann zeta function | p. 178 |
| Some generalizations related to Bessel processes | p. 178 |
| Some relations between X[superscript v] and [Sigma superscript v-1] [identical with] [sigma subscript v-1] + [sigma]'[subscript v-1] | p. 182 |
| [zeta superscript v](s) as a function of v | p. 186 |
| References | p. 189 |
| Further general references about BM and Related Processes | p. 195 |
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