Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

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Methods Of Modern Mathematical Physics

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Lie groups and Lie algebras (chapters 1-3 ), by N. Bourbaki. Pp 450. DM 98. 1989. ISBN 3-540-50218-1 (Springer)

Free Random Variables

Dans cet article, nous definissons une notion de cumulants generalises qui fournit un cadre commun pour les theories de probabilites commutatives, libres, booleennes et monotones. L’unicite des cumulants generalises est verifiee pour chacune de ces notions d’independance, qui par consequent coincident avec les cumulants usuels dans les cadres commutatifs, libres et booleen. La facon dont nous definissons ces cumulants ne necessite ni partition de reseaux ni fonction generatrice et donne un nouveau point de vue sur ces cumulants. Nous definissons des “cumulants monotones” et obtenons des preuves assez simples des theoremes de la limite centrale et de la distribution de Poisson dans le contexte des probabilites monotones. De plus, nous clarifions une structure combinatoire de la relation moments-cumulants a l’aide des “partitions monotones”.

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The monotone cumulants

Relations between cumulants in noncommutative probability

In the present paper we define the notion of generalized cumulants which gives a universal framework for commutative, free, Boolean, and especially, monotone probability theories. The uniqueness of generalized cumulants holds for each independence, and hence, generalized cumulants are equal to the usual cumulants in the commutative, free and Boolean cases. The way we define (generalized) cumulants needs neither partition lattices nor generating functions and then will give a new viewpoint to cumulants. We define ``monotone cumulants'' in the sense of generalized cumulants and we obtain quite simple proofs of central limit theorem and Poisson's law of small numbers in monotone probability theory. Moreover, we clarify a combinatorial structure of moment-cumulant formula with the use of ``monotone partitions''.

The Monotone Cumulants

Fock space associated to Coxeter groups of type B

We study the freely infinitely divisible distributions that appear as the laws of free subordinators. This is the free analog of classically infinitely divisible distributions supported on [0,\infty), called the free regular measures. We prove that the class of free regular measures is closed under the free multiplicative convolution, t-th boolean power for $0\leq t\leq 1$, t-th free multiplicative power for $t\geq 1$ and weak convergence. In addition, we show that a symmetric distribution is freely infinitely divisible if and only if its square can be represented as the free multiplicative convolution of a free Poisson and a free regular measure. This gives two new explicit examples of distributions which are infinitely divisible with respect to both classical and free convolutions: \chi^2(1) and F(1,1). Another consequence is that the free commutator operation preserves free infinite divisibility.

Takahiro Hasebe

Papers

The monotone cumulants

Relations between cumulants in noncommutative probability

The Monotone Cumulants

Fock space associated to Coxeter groups of type B

On the Law of Free Subordinators