Existence, Uniqueness and Regularity of Decoupling Fields to Multidimensional Fully Coupled FBSDEs

We develop an existence, uniqueness and regularity theory for general multidimensional strongly coupled FBSDE using so called decoupling fields. We begin with a local result and extend it to a global theory via concatenation. The cornerstone of the global theory is the so called maximal interval which is, roughly speaking, the largest interval on which reasonable solutions exist. A method to verify that the maximal interval is the whole interval, for problems in which this is conjectured, is proposed. As part of our study of the regularity of solutions constructed we show variational differentiability under Lipschitz assumptions. Extra emphasis is put on the more special Markovian case in which assumptions on the Lipschitz continuity for the FBSDE can be weakened to local ones, and additional regularity properties emerge

Verbesserrung der Datenflussüberwachung für Datennutzungskontrollsysteme

This thesis provides a new, hybrid approach in the field of Distributed Data Usage Control (DUC), to track the flow of data inside applications. A combination between static information flow analysis and dynamic data flow tracking enables to track selectively only those program locations that are actually relevant for a flow of data. This ensures the portability of a monitored application with low performance overhead. Beyond that, DUC systems benefit from the present approach as it reduces overapproximation in data flow tracking, and thus, provides a more precise result to enforce data usage restrictions.Diese Thesis liefert einen neuartigen hybriden Ansatz auf dem Gebiet von Distributed Data Usage Control (DUC), um den Datenfluss innerhalb einer Anwendung zu überwachen. Eine Kombination aus statischer Informationsflussanalyse und dynamischer Datenflussüberwachung ermöglicht die selektive, modulare Überwachung derjenigen Programmstellen, welche tatsächlich relevant für einen Datenfluss sind. Dadurch wird die Portabilität einer zu überwachenden Anwendung, bei geringem Performance Overhead, sichergestellt. DUC Systeme profitieren vom vorliegenden Ansatz vor allem dadurch, dass Überapproximation bei der Datenflussüberwachung reduziert wird, und somit ein präziseres Ergebnis für die Durchsetzung von Datennutzungsrestriktionen vorliegt

An FBSDE approach to the Skorokhod embedding problem for Gaussian processes with non-linear drift

We solve the Skorokhod embedding problem for a class of Gaussian processes including Brownian motion with non-linear drift. Our approach relies on solving an associated strongly coupled system of Forward Backward Stochastic Differential Equation (FBSDE), and investigating the regularity of the obtained solution. For this purpose we extend the existence, uniqueness and regularity theory of so called decoupling fields for Markovian FBSDE to a setting in which the coefficients are only locally Lipschitz continuous

Improved AdS/QCD Model with Matter

We study an improved AdS/QCD model at finite temperature and chemical potential. An Ansatz for the beta-function for the boundary theory allows for the derivation of a charged dilatonic black hole in bulk. The solution is asymptotically RN-AdS in the UV and AdS2 * R3 in the IR. We discuss the thermodynamical aspects of the solution. The fermionic susceptibilities are shown to deviate from the free fermionic limits at asymptotic temperatures despite the asymptotically free nature of the gauge coupling at the boundary. The Polyakov line, the temporal and spatial string tensions dependence on both temperature and chemical potential are also discussed

A transformation method to study the solvability of fully coupled FBSDEs

We present a new method for checking global solvability of fully coupled forward-backward stochastic differential equations (FBSDEs), where all function parameters are Lipschitz continuous, the terminal condition is monotone and the diffusion coefficient of the forward part depends monotonically on z, the control process component of the backward part. We show that one can reduce, via a linear transformation, the FBSDE to an auxiliary FBSDE for which the Lipschitz constant of the forward diffusion coefficient w.r.t. z is smaller than the inverse of the Lipschitz constant of the terminal condition w.r.t. the forward component x. The latter condition allows to verify existence of a global solution by analyzing the space derivative of the decoupling field. We illustrate with several examples how the transformation method can be used for proving global solvability of FBSDEs

The Skorokhod embedding problem for inhomogeneous diffusions

We solve the Skorokhod embedding problem for a class of stochastic processes satisfying an inhomogeneous stochastic differential equation (SDE) of the form $d A_t =\mu (t, A_t) d t + \sigma(t, A_t) d W_t$. We provide sufficient conditions guaranteeing that for a given probability measure $\nu$ on $\mathbb{R}$ there exists a bounded stopping time $\tau$ and a real $a$ such that the solution $(A_t)$ of the SDE with initial value $a$ satisfies $A_\tau \sim \nu$. We hereby distinguish the cases where $(A_t)$ is a solution of the SDE in a weak or strong sense. Our construction of embedding stopping times is based on a solution of a fully coupled forward-backward SDE. We use the so-called method of decoupling fields for verifying that the FBSDE has a unique solution. Finally, we sketch an algorithm for putting our theoretical construction into practice and illustrate it with a numerical experiment.Comment: 39 pages, 2 pictures, To appear in Annales de l'Institut Henri Poincare (B) Probability and Statistic