Renewal processes with random numbers of delays: application to a conception and birth model

1978 ◽  
Vol 15 (02) ◽  
pp. 209-224
Author(s):  
Kenneth Lange ◽  
Norman J. Johnson
Keyword(s):  
Birth Control ◽  
Renewal Process ◽  
Random Number ◽  
Asymptotic Formulas ◽  
Random Numbers ◽  
Renewal Processes ◽  
Demographic Model ◽  
Two Stage ◽  
Live Births ◽  
Stieltjes Transforms

Asymptotic formulas and Laplace–Stieltjes transforms are derived for the first two moments of a renewal process with a random number of delays. These are simplified when all the delays follow the same distribution. An asymptotic occupancy result is also derived for two-stage renewal processes with random numbers of delays. As an example, a demographic model of conception and birth is discussed. This model represents the sequence of live births to a woman as a renewal process. If the woman practises birth control after achieving her desired family composition, the renewal process has a random number of delays.

Renewal processes with random numbers of delays: application to a conception and birth model

1978 ◽  
Vol 15 (2) ◽  
pp. 209-224 ◽  
Author(s):  
Kenneth Lange ◽  
Norman J. Johnson
Keyword(s):  
Birth Control ◽  
Renewal Process ◽  
Random Number ◽  
Asymptotic Formulas ◽  
Random Numbers ◽  
Renewal Processes ◽  
Demographic Model ◽  
Two Stage ◽  
Live Births ◽  
Stieltjes Transforms

Asymptotic formulas and Laplace–Stieltjes transforms are derived for the first two moments of a renewal process with a random number of delays. These are simplified when all the delays follow the same distribution. An asymptotic occupancy result is also derived for two-stage renewal processes with random numbers of delays. As an example, a demographic model of conception and birth is discussed. This model represents the sequence of live births to a woman as a renewal process. If the woman practises birth control after achieving her desired family composition, the renewal process has a random number of delays.

scholarly journals A Hardware Pseudo-Random Number Generator Using Stochastic Computing and Logistic Map

Micromachines ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 31
Author(s):  
Junxiu Liu ◽  
Zhewei Liang ◽  
Yuling Luo ◽  
Lvchen Cao ◽  
Shunsheng Zhang ◽  
...  
Keyword(s):  
Random Number ◽  
Chaotic Map ◽  
Logistic Map ◽  
Random Number Generator ◽  
Alternative Methods ◽  
Random Numbers ◽  
Number Generator ◽  
Stochastic Computing ◽  
Pseudo Random Number ◽  
Pseudo Random Number Generator

Recent research showed that the chaotic maps are considered as alternative methods for generating pseudo-random numbers, and various approaches have been proposed for the corresponding hardware implementations. In this work, an efficient hardware pseudo-random number generator (PRNG) is proposed, where the one-dimensional logistic map is optimised by using the perturbation operation which effectively reduces the degradation of digital chaos. By employing stochastic computing, a hardware PRNG is designed with relatively low hardware utilisation. The proposed hardware PRNG is implemented by using a Field Programmable Gate Array device. Results show that the chaotic map achieves good security performance by using the perturbation operations and the generated pseudo-random numbers pass the TestU01 test and the NIST SP 800-22 test. Most importantly, it also saves 89% of hardware resources compared to conventional approaches.

scholarly journals Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 55
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Renewal Process ◽  
Markov Chain Model ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Chain Model ◽  
Markov Renewal Processes ◽  
Risky Bonds ◽  
Markov Structure

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

scholarly journals Design of True Random Number Circuit with Controllable Frequency

Electronics ◽  
2021 ◽  
Vol 10 (13) ◽  
pp. 1517
Author(s):  
Xinsheng Wang ◽  
Xiyue Wang
Keyword(s):  
Random Number ◽  
Noise Source ◽  
State Of The Art ◽  
Building Blocks ◽  
Encryption Algorithm ◽  
Random Numbers ◽  
Random Number Generators ◽  
Random Telegraph Noise ◽  
Telegraph Noise ◽  
Novel Method

True random number generators (TRNGs) have been a research hotspot due to secure encryption algorithm requirements. Therefore, such circuits are necessary building blocks in state-of-the-art security controllers. In this paper, a TRNG based on random telegraph noise (RTN) with a controllable rate is proposed. A novel method of noise array circuits is presented, which consists of digital decoder circuits and RTN noise circuits. The frequency of generating random numbers is controlled by the speed of selecting different gating signals. The results of simulation show that the array circuits consist of 64 noise source circuits that can generate random numbers by a frequency from 1 kHz to 16 kHz.

scholarly journals RRAM Random Number Generator Based on Train of Pulses

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1831
Author(s):  
Binbin Yang ◽  
Daniel Arumí ◽  
Salvador Manich ◽  
Álvaro Gómez-Pau ◽  
Rosa Rodríguez-Montañés ◽  
...  
Keyword(s):  
Random Number ◽  
Random Number Generator ◽  
Random Access ◽  
Pulse Amplitude ◽  
Resistive Random Access Memory ◽  
Random Numbers ◽  
Number Generator ◽  
Security Applications ◽  
Device Resistance ◽  
New Strategy

In this paper, the modulation of the conductance levels of resistive random access memory (RRAM) devices is used for the generation of random numbers by applying a train of RESET pulses. The influence of the pulse amplitude and width on the device resistance is also analyzed. For each pulse characteristic, the number of pulses required to drive the device to a particular resistance threshold is variable, and it is exploited to extract random numbers. Based on this behavior, a random number generator (RNG) circuit is proposed. To assess the performance of the circuit, the National Institute of Standards and Technology (NIST) randomness tests are applied to evaluate the randomness of the bitstreams obtained. The experimental results show that four random bits are simultaneously obtained, passing all the applied tests without the need for post-processing. The presented method provides a new strategy to generate random numbers based on RRAMs for hardware security applications.

Large deviations of generalized renewal process

2020 ◽  
Vol 30 (4) ◽  
pp. 215-241
Author(s):  
Gavriil A. Bakay ◽  
Aleksandr V. Shklyaev
Keyword(s):  
Large Deviations ◽  
Renewal Process ◽  
Limit Theorems ◽  
Local Limit ◽  
Asymptotic Formulas ◽  
Additive Functionals ◽  
Wide Range ◽  
Finite Markov Chains ◽  
Independent Identically Distributed ◽  
Local Limit Theorems

AbstractLet (ξ(i), η(i)) ∈ ℝd+1, 1 ≤ i < ∞, be independent identically distributed random vectors, η(i) be nonnegative random variables, the vector (ξ(1), η(1)) satisfy the Cramer condition. On the base of renewal process, NT = max{k : η(1) + … + η(k) ≤ T} we define the generalized renewal process ZT = $\begin{array}{} \sum_{i=1}^{N_T} \end{array}$ξ(i). Put IΔT(x) = {y ∈ ℝd : xj ≤ yj < xj + ΔT, j = 1, …, d}. We find asymptotic formulas for the probabilities P(ZT ∈ IΔT(x)) as ΔT → 0 and P(ZT = x) in non-lattice and arithmetic cases, respectively, in a wide range of x values, including normal, moderate, and large deviations. The analogous results were obtained for a process with delay in which the distribution of (ξ(1), η(1)) differs from the distribution on the other steps. Using these results, we prove local limit theorems for processes with regeneration and for additive functionals of finite Markov chains, including normal, moderate, and large deviations.

A characterization of the Poisson process

1974 ◽  
Vol 11 (1) ◽  
pp. 72-85 ◽  
Author(s):  
S. M. Samuels
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Poisson Processes ◽  
Renewal Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Proof ◽  
Necessary And Sufficient

Theorem: A necessary and sufficient condition for the superposition of two ordinary renewal processes to again be a renewal process is that they be Poisson processes.A complete proof of this theorem is given; also it is shown how the theorem follows from the corresponding one for the superposition of two stationary renewal processes.

scholarly journals Introduction to Stochastic Computing using a Remote Lab with Reconfigurable Logic

2016 ◽  
Vol 12 (04) ◽  
pp. 23
Author(s):  
Jorge Lobo
Keyword(s):  
Random Number ◽  
Random Number Generation ◽  
Linear Feedback ◽  
Short Paper ◽  
Integration Time ◽  
Random Numbers ◽  
Reconfigurable Logic ◽  
Linear Feedback Shift Registers ◽  
Stochastic Computing ◽  
Remote Lab

This short paper introduces the basic concepts of Stochastic Computing (SC), and presents additions to a remote lab with reconfigurable logic to allow testing SC circuits. Recently, SC has been revisited and evaluated as a possible way of performing approximate probabilistic computations for artificial perception systems. New modules allow the generation of pseudo-random numbers, given a seed key and using linear feedback shift registers, but also having true random number generation using ring oscillators and embedded PLLs. Stochastic computing allows a tradeoff between resource usage and precision, allowing very simple circuits to perform computations, at the expense of a longer integration time to have reasonable results. We provide the basic stochastic computing modules, so that any user can use them to build a stochastic computing circuit and go beyond software simulations, providing a remote hardware device to test real circuits at high clock speeds.

scholarly journals Problem of uniqueness in the renewal process generated by the uniform distribution

1992 ◽  
Vol 5 (4) ◽  
pp. 291-305 ◽  
Author(s):  
D. Ugrin-Šparac
Keyword(s):  
Integral Representation ◽  
Uniform Distribution ◽  
Gamma Function ◽  
Renewal Process ◽  
Random Number ◽  
Discrete Distribution ◽  
Inverse Image ◽  
Random Number Generators ◽  
Pseudo Random Number

The renewal process generated by the uniform distribution, when interpreted as a transformation of the uniform distribution into a discrete distribution, gives rise to the question of uniqueness of the inverse image. The paper deals with a particular problem from the described domain, that arose in the construction of a complex stochastic test intended to evaluate pseudo-random number generators. The connection of the treated problem with the question of a unique integral representation of Gamma-function is also mentioned.

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