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SPRNG: A Scalable Library for Pseudorandom Number Generation
"... In this article we present background, rationale, and a description of the Scalable Parallel Random
Number Generators (SPRNG) library. We begin by presenting some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not conside ..."
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Cited by 38 (6 self)
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In this article we present background, rationale, and a description of the Scalable Parallel Random
Number Generators (SPRNG) library. We begin by presenting some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not consider splitting methods such as the leapfrog or blocking methods. We describe in detail
parameterized versions of the following pseudorandom number generators: (i) linear congruential
generators, (ii) shiftregister generators, and (iii) laggedFibonacci generators. We briey describe
the methods, detail some advantages and disadvantages of each method, and recount results from
number theory that impact our understanding of their quality in parallel applications.
SPRNG was designed around the uniform implementation of dierent families of parameterized random number
generators. We then present a short description of
SPRNG. The description contained within this
document is meant only to outline the rationale behind and the capabilities of SPRNG. Much more
information, including examples and detailed documentation aimed at helping users with putting
and using SPRNG on scalable systems is available at the URL:
http://sprng.cs.fsu.edu/RNG. In this description of SPRNG we discuss the random number generator library as well as the suite of
tests of randomness that is an integral part of SPRNG. Random number tools for parallel Monte
Carlo applications must be subjected to classical as well as new types of empirical tests of ran
domness to eliminate generators that show defects when used in scalable environments.
Linear Congruential Generators for Parallel MonteCarlo: the LeapFrog Case.
 Monte Carlo Methods and Applications
, 1997
"... In this paper we consider parallel streams of pseudorandom numbers (PRNs) which are obtained by splitting linear congruential generators (LCGs) using the leapfrog technique. We employ the spectral test to compute an a priori figure of merit which rates the amount of correlation that is present in s ..."
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Cited by 7 (4 self)
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In this paper we consider parallel streams of pseudorandom numbers (PRNs) which are obtained by splitting linear congruential generators (LCGs) using the leapfrog technique. We employ the spectral test to compute an a priori figure of merit which rates the amount of correlation that is present in such sequences for given step size and dimension. It is shown that for some widely used LCGs there exist practically relevant splitting parameters such that the according parallel streams have poor quality. As can be seen from a sample MonteCarlo integration study, these theoretical findings have high practical importance. 1 Introduction Parallel computations in the field of stochastic simulation (e.g. [14, 9]) require a source of pseudorandom numbers (PRNs) which can be distributed among the single processing units. This is most efficiently achieved by assigning a generator to each such processing unit [15]. In order to be able to Research supported by the Austrian Science Foundation (FW...
Parallel Monte Carlo Methods for Derivative Security Pricing
 In Computing in Economics, Finance 2000
, 2000
"... Monte Carlo (MC) methods have proved to be flexible, robust and very useful techniques in computational finance. Several studies have investigated ways to achieve greater efficiency of such methods for serial computers. In this paper, we concentrate on the parallelization potentials of the MC method ..."
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Cited by 4 (0 self)
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Monte Carlo (MC) methods have proved to be flexible, robust and very useful techniques in computational finance. Several studies have investigated ways to achieve greater efficiency of such methods for serial computers. In this paper, we concentrate on the parallelization potentials of the MC methods. While MC is generally thought to be "embarrassingly parallel", the results eventually depend on the quality of the underlying parallel pseudorandom number generators. There are several methods for obtaining pseudorandom numbers on a parallel computer and we briefly present some alternatives. Then, we turn to an application of security pricing where we empirically investigate the pros and cons of the different generators. This also allows us to assess the potentials of parallel MC in the computational finance framework.
A Multiple Stream Generator Based on De Bruijn Digraph Homomorphisms
 Journal of Statistical Computing and Simulation
"... Abstract. We propose a method to obtain several streams of bits based on an original backbone generalized shift register type generator. The method is based on inverting one cycle in a de Bruijn digraph into many sequences in a higher order de Bruijn graph via an appropriate graph homomorphism. We a ..."
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Cited by 1 (1 self)
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Abstract. We propose a method to obtain several streams of bits based on an original backbone generalized shift register type generator. The method is based on inverting one cycle in a de Bruijn digraph into many sequences in a higher order de Bruijn graph via an appropriate graph homomorphism. We apply this technique to twisted generalized feedback shift register generators and to the Mersenne Twister MT19937. Results of statistical tests are reported. 1.
Dedication
"... This work is dedicated to my family: my parents, my sister and my grandmother iii Acknowledgments I would like to thank my advisor Dr. Zafer Boybeyi, who provided me the opportunity to embark upon this journey. Without his continuous moral and scientific support at every level, this work would not h ..."
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This work is dedicated to my family: my parents, my sister and my grandmother iii Acknowledgments I would like to thank my advisor Dr. Zafer Boybeyi, who provided me the opportunity to embark upon this journey. Without his continuous moral and scientific support at every level, this work would not have been possible. Taking on the rather risky move of giving me 100 % freedom in research from the beginning certainly deserves my greatest acknowledgments. I am also thoroughly indebted to Dr. Pasquale Franzese for his guidance of this research, for the many lengthy – sometimes philosophical – discussions on turbulence and other topics, for being always available and for his painstaking drive with me through the dungeons of research, scientific publishing and aesthetics. My gratitude extends to Dr. Rainald Löhner from whom I had the opportunity to take classes in CFD and to learn how not to get lost in the details. I found his weekly seminars to be one of the best opportunities to learn critical and downtoearth thinking. I am also indebted to Dr. Nash’at Ahmad for showing me the example that with a careful balance of school, hard work and family nothing is impossible. I thank Dr. Thomas Dreeben for the many helpful and insightful discussions on the velocity model and elliptic relaxation. I am also grateful to the reviewers of our journal papers for their valuable comments and suggestions on our initial manuscripts. I will always remember my professors at home at the Departments of Mathematics,
Author manuscript, published in "Monte Carlo Methods and Applications (2013) 23 pages" DOI: 10.1515/mcma20130001 A Parallel Algorithm for solving BSDEs
, 2013
"... We present a parallel algorithm for solving backward stochastic differential equations. We improve the algorithm proposed in Gobet and Labart (2010), based on an adaptive Monte Carlo method with Picard’s iterations, and propose a parallel version of it. We test our algorithm on linear and non linear ..."
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We present a parallel algorithm for solving backward stochastic differential equations. We improve the algorithm proposed in Gobet and Labart (2010), based on an adaptive Monte Carlo method with Picard’s iterations, and propose a parallel version of it. We test our algorithm on linear and non linear drivers up to dimension 8 on a cluster of 312 CPUs. We obtained very encouraging efficiency ratios greater than 0.7.
A Parallel TraceforwardTraceback Simulation at Large Scale
, 2007
"... In April 2006 the USDAAPHIS released a voluntary animal identification and traceability framework collectively known as the National Animal Identification System (NAIS). The basic goal of the NAIS program is to associate a unique identifier (animal ID) to every element of commercial livestock in th ..."
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In April 2006 the USDAAPHIS released a voluntary animal identification and traceability framework collectively known as the National Animal Identification System (NAIS). The basic goal of the NAIS program is to associate a unique identifier (animal ID) to every element of commercial livestock in the United
1 A Parallel Algorithm for solving BSDEs Application to the pricing and hedging of American options
, 2013
"... ar ..."
A Parallel Algorithm for solving BSDEs
, 2013
"... We present a parallel algorithm for solving backward stochastic differential equations. We improve the algorithm proposed in Gobet and Labart (2010), based on an adaptive Monte Carlo method with Picard’s iterations, and propose a parallel version of it. We test our algorithm on linear and non linear ..."
Abstract
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We present a parallel algorithm for solving backward stochastic differential equations. We improve the algorithm proposed in Gobet and Labart (2010), based on an adaptive Monte Carlo method with Picard’s iterations, and propose a parallel version of it. We test our algorithm on linear and non linear drivers up to dimension 8 on a cluster of 312 CPUs. We obtained very encouraging efficiency ratios greater than 0.7.