On the Superposition of Renewal Processes

Cox, David; Smith, Walter L.

doi:10.1093/biomet/41.1-2.91

Cited by 204 publications

(95 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…30 The latter is verified against exact stochastic simulations based on the Doob-Gillespie 4 algorithm. 31−34 The calculation of the waiting time distribution for the first product formation belongs to a general class of first-passage problems in stochastic processes.…”

Section: Introductionmentioning

confidence: 88%

“…This approach, based on the superposition of renewal processes (SRP), was first introduced by Cox and Smith to understand the statistical properties of discrete neuron signals in neurophysiology. 30 The SRP method exploits the renewal nature of statistical properties of the sequence of impulses from an individual neuron to obtain a single pooled output. The latter corresponds to the combined sequence of pulses at the central cell.…”

Section: Concentrationsmentioning

confidence: 99%

See 1 more Smart Citation

Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

Kumar

Chatterjee

Nandi

et al. 2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

Dynamic cooperativity in monomeric enzymes is characterized in terms of a non-Michaelis-Menten kinetic behaviour. The latter is believed to be associated with mechanisms that include multiple reaction pathways due to enzymatic conformational fluctuations. Recent advances in single-molecule fluorescence spectroscopy have provided new fundamental insights on the possible mechanisms underlying reactions catalyzed by fluctuating enzymes. Here, we present a bottom-up approach to understand enzyme turnover kinetics at physiologically relevant mesoscopic concentrations informed by mechanisms extracted from single-molecule stochastic trajectories. The stochastic approach, presented here, shows the emergence of dynamic cooperativity in terms of a slowing down of the Michaelis-Menten (MM) kinetics resulting in negative cooperativity. For fewer enzymes, dynamic cooperativity emerges due to the combined effects of enzymatic conformational fluctuations and molecular discreteness. The increase in the number of enzymes, however, suppresses the effect of enzymatic conformational fluctuations such that dynamic cooperativity emerges solely due to the discrete changes in the number of reacting species. These results confirm that the turnover kinetics of fluctuating enzyme based on the parallel-pathway MM mechanism switches over to the singlepathway MM mechanism with the increase in the number of enzymes. For large enzyme numbers, convergence to the exact MM equation occurs in the limit of very high substrate concentration as the stochastic kinetics approaches the deterministic behaviour.

show abstract

Section: Introductionmentioning

confidence: 88%

Section: Concentrationsmentioning

confidence: 99%

Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

Kumar

Chatterjee

Nandi

et al. 2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…This follows from a classical result on multiplexing a large number of renewal processes [COS54,CIN72].…”

Section: Infinite Number Of On-off Processesmentioning

confidence: 96%

Asymptotic results for multiplexing subexponential on-off processes

Jelenković

Lazar

1999

Adv. Appl. Probab.

View full text Add to dashboard Cite

Consider an aggregate arrival process A N obtained by multiplexing N On-Off processes with exponential Off periods of rate λ and subexponential On periods τ on . As N goes to infinity, with λN → Λ, A N approaches an M/G/∞ type process. Both for finite and infinite N , we obtain the asymptotic characterization of the arrival process activity period.Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process A ∞ t and capacity c. When On periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable Q P t observed at the beginning of the arrival process activity periodswhere ρ = EA ∞ t < c; r (c ≤ r) is the rate at which the fluid is arriving during an On period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions on On periods than regular variation.In addition, we analyze a queueing system in which one On-Off process, whose On period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate Ee t . This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value Ee t .

show abstract

“…If we superposition (Cox and Smith, 1954) M independent and identical Bernoulli sequences X i,t , i = 1, 2, . .…”

Section: Renewal Count Processesmentioning

confidence: 99%

Binomial ARMA count series from renewal processes

Koshkin

Cui

2012

Discuss. Math. Probability and Statistics

View full text Add to dashboard Cite

This paper describes a new method for generating stationary integer-valued time series from renewal processes. We prove that if the lifetime distribution of renewal processes is nonlattice and the probability generating function is rational, then the generated time series satisfy causal and invertible ARMA type stochastic difference equations. The result provides an easy method for generating integer-valued time series with ARMA type autocovariance functions. Examples of generating binomial ARMA(p, p − 1) series from lifetime distributions with constant hazard rates after lag p are given as an illustration. An estimation method is developed for the AR(p) cases.

show abstract

On the Superposition of Renewal Processes

Cited by 204 publications

References 0 publications

Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

Emergence of dynamic cooperativity in the stochastic kinetics of fluctuating enzymes

Asymptotic results for multiplexing subexponential on-off processes

Binomial ARMA count series from renewal processes

Contact Info

Product

Resources

About