In this paper we consider an analytical valuation of Basket Default Swaps. Our solution is based on a continuous-time model in a conditional independence framework. We use the order statistics of the default times of the names in the basket to find a recursive algorithm for computation of the risk-neutral distribution of the default process of the basket. We derive an analytical expression for ...

This paper presents a symbolic and recursive calculation of the stiffness and mass matrices of parallel robots. In order to reduce the computational time required for simulating the elastodynamic behavior of robots, it is necessary to minimize the number of operators in the symbolic model expression. Some algorithms have been proposed for the rigid case or for parallel robots with lumped spring...

We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive variants, and compare feasibility as a function of the total computation burden. We identify trade-offs between the different methods depending on the problem stru...

This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...

Abstract We define a class of computable functions over real numbers using functional schemes similar to the primitive and partial recursive defined by Gödel (1931, 1934) Kleene (1936, Math. Ann., 112, 727–742). show that this can also be characterized MS-machines, which are Turing machine-like devices. The proof characterization gives normal form theorem in style Furthermore, is natural combin...

An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these notions as a very simple algebraic system, called a configuration machine. If an abstract machine is defined as a configuration machine consisting of primitive...

The authors develop a self-contained theory for linear estimation in Krein spaces. The derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between Krein space projection and the recursive computation of the stationary points of certain second-order (or quadratic) forms. The authors use the innovations process to obtain a ge...

A general framework is presented for recursive computation of image local statistics in sliding window of almost arbitrary shape with “per-pixel” computational complexity substantially lower than the window size. As special cases, recursive algorithms are described for computing image local statistics such as local mean, local variance, local kurtosis, local order statistics (minimum, maximum, ...

As an alternative local and higher order algorithm, the parallel recursive prediction error algorithm (PRPE) is used to train the recurrent neural networks (RNNs). This algorithm uses a modiied form of the well-known recursive prediction error algorithm (RPE) such that the computation can be distributed into each node in the network. Therefore, the algorithm has a better trade-oo between comput...

&tract. Various forms of polynomial time reducibilig:y zwe compared. Among the forms examined we many-one, bounded truth table, truth 1:able and Turing reducibi!&y. The effect of introducing nondeterminism into red " ,ztiGn procedures is also examined. Computation bounded reducibilities play a role in t theory of' ssralputationa~ complexity which is analogous to, and perhaps as important as, th...