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

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. The stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with additive noise 6. Linear equations with multiplicative noise 7. Existence and uniqueness for nonlinear equations 8. Martingale solutions Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations 10. Absolute continuity and Girsanov's theorem 11. Large time behaviour of solutions 12. Small noise asymptotic.

Stochastic Equations in Infinite Dimensions

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

We define three types of non causal stochastic integrals: forward, backward and symmetric. Our approach consists in approximating the integrator. Two optics are considered: the first one is based on traditional usual stochastic calculus and the second one on Wiener distributions.

Forward, backward and symmetric stochastic integration

The quadratic variation of a continuous process (when it exists) is defined through a regularization procedure. A large class of finite quadratic variation processes is provided, with a particular emphasis on Gaussian processes. For such processes a calculus is developed with application to the study of some stochastic differential equations.

Stochastic calculus with respect to continuous finite quadratic variation processes

The generalized covariation process and Ito formula

This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure Ito and Stratonovich integrals In the second part, a survey and new results are presented in relation with finite quadratic variation processes, Dirichlet and weak Dirichlet processes

/pdf/elements-of-stochastic-calculus-via-regularization-3wcasanh0q.pdf

Elements of Stochastic Calculus via Regularization

https://bibos.math.uni-bielefeld.de/preprints/05-03-177.pdf

Francesco Russo

Papers

Forward, backward and symmetric stochastic integration

Stochastic calculus with respect to continuous finite quadratic variation processes

The generalized covariation process and Ito formula

Elements of Stochastic Calculus via Regularization

On bifractional Brownian motion