Stochastic Differential Equations and Random Number Generators Minimize Numerical Instabilities in Digital Simulations

Author(s):  
Walter J. Freeman
2014 ◽  
Vol 29 ◽  
pp. 172-183 ◽  
Author(s):  
Christoph Riesinger ◽  
Tobias Neckel ◽  
Florian Rupp ◽  
Alfredo Parra Hinojosa ◽  
Hans-Joachim Bungartz

2008 ◽  
Vol 08 (03) ◽  
pp. 561-581 ◽  
Author(s):  
NICOLA BRUTI-LIBERATI ◽  
ECKHARD PLATEN

This paper introduces a new class of numerical schemes for the pathwise approximation of solutions of stochastic differential equations (SDEs). The proposed family of strong predictor–corrector Euler methods are designed to handle scenario simulation of solutions of SDEs. It has the potential to overcome some of the numerical instabilities that are often experienced when using the explicit Euler method. This is of importance, for instance, in finance where martingale dynamics arise for solutions of SDEs with multiplicative diffusion coefficients. Numerical experiments demonstrate the improved asymptotic stability properties of the proposed symmetric predictor–corrector Euler methods.


2012 ◽  
Author(s):  
Bo Jiang ◽  
Roger Brockett ◽  
Weibo Gong ◽  
Don Towsley

2020 ◽  
Vol 53 (2) ◽  
pp. 2220-2224
Author(s):  
William M. McEneaney ◽  
Hidehiro Kaise ◽  
Peter M. Dower ◽  
Ruobing Zhao

Cryptography ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Bertrand Cambou ◽  
Donald Telesca ◽  
Sareh Assiri ◽  
Michael Garrett ◽  
Saloni Jain ◽  
...  

Schemes generating cryptographic keys from arrays of pre-formed Resistive Random Access (ReRAM) cells, called memristors, can also be used for the design of fast true random number generators (TRNG’s) of exceptional quality, while consuming low levels of electric power. Natural randomness is formed in the large stochastic cell-to-cell variations in resistance values at low injected currents in the pre-formed range. The proposed TRNG scheme can be designed with three interconnected blocks: (i) a pseudo-random number generator that acts as an extended output function to generate a stream of addresses pointing randomly at the array of ReRAM cells; (ii) a method to read the resistance values of these cells with a low injected current, and to convert the values into a stream of random bits; and, if needed, (iii) a method to further enhance the randomness of this stream such as mathematical, Boolean, and cryptographic algorithms. The natural stochastic properties of the ReRAM cells in the pre-forming range, at low currents, have been analyzed and demonstrated by measuring a statistically significant number of cells. Various implementations of the TRNGs with ReRAM arrays are presented in this paper.


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