A stochastic model for time lag in reporting of claims

1974 ◽  
Vol 11 (2) ◽  
pp. 382-387 ◽  
Author(s):  
Jan-Erik Karlsson
Keyword(s):  
Integral Equation ◽  
Stochastic Model ◽  
Renewal Process ◽  
Value Function ◽  
Time Lag ◽  
Mean Value ◽  
Time Interval ◽  
Asymptotic Expressions ◽  
The Laplace Transform ◽  
The Mean

We assume that the number of claims occur according to a renewal process and treat the number of claims that occur and are reported in a certain time interval as a renewal process with random displacements. We obtain a renewal equation for the mean value function and an integral equation for the Laplace transform of the distribution of the claims that are reported. We also give asymptotic expressions for the mean value function and calculate the generating function in the case where the renewal process is a Poisson process. This matter is a part of the IBNR-problem in insurance mathematics.

A stochastic model for time lag in reporting of claims

1974 ◽  
Vol 11 (02) ◽  
pp. 382-387 ◽  
Author(s):  
Jan-Erik Karlsson
Keyword(s):  
Integral Equation ◽  
Stochastic Model ◽  
Renewal Process ◽  
Value Function ◽  
Time Lag ◽  
Mean Value ◽  
Time Interval ◽  
Asymptotic Expressions ◽  
The Laplace Transform ◽  
The Mean

We assume that the number of claims occur according to a renewal process and treat the number of claims that occur and are reported in a certain time interval as a renewal process with random displacements. We obtain a renewal equation for the mean value function and an integral equation for the Laplace transform of the distribution of the claims that are reported. We also give asymptotic expressions for the mean value function and calculate the generating function in the case where the renewal process is a Poisson process. This matter is a part of the IBNR-problem in insurance mathematics.

Realisation of the mean-value function

1973 ◽  
Vol 9 (22) ◽  
pp. 528
Author(s):  
E. Ball
Keyword(s):  
Value Function ◽  
Mean Value ◽  
The Mean

Initiation of each avian inspiration by a CO2 threshold mechanism

1979 ◽  
Vol 47 (1) ◽  
pp. 233-239 ◽  
Author(s):  
D. A. Miller ◽  
A. L. Kunz
Keyword(s):  
Threshold Model ◽  
Co2 Concentration ◽  
Threshold Level ◽  
Mean Value ◽  
Wave Form ◽  
Time Interval ◽  
Threshold Mechanism ◽  
The Mean ◽  
The Relationship ◽  
Respiratory Movements

The avian respiratory oscillator has been investigated in a unidirectionally ventilated chicken by changing the dynamic pattern of inflow CO2 concentration (FCO2). Stimulation with periodic FCO2 results in a one-to-one synchronization of the respiratory movements that we have called pacing (Respir. Physiol. 22: 167--177, 1974). A two-parameter CO2 threshold model is proposed to explain this behavior. The model states that when FCO2 reaches a threshold level (L), it initiates the beginning of inspiration a constant time interval (LB) later. According to this model, when a triangular FCO2 concentration is used to synchronize the breathing pattern, the time from the minimum of the wave form to the beginning of inspiration (C-B interval) is dependent on the mean value and the rate of rise of FCO2 as determined by period and amplitude of the triangle. Particularly interesting is the prediction that the direction of the relationship (increasing or decreasing) between FCO2 amplitude and the C-B interval is dependent on whether the mean value of FCO2 is above or below the threshold level. Experimental data obtained during amplitude changes support the above prediction.

On the mean field approximation of a stochastic model of tumour-induced angiogenesis

2018 ◽  
Vol 30 (04) ◽  
pp. 619-658 ◽  
Author(s):  
V. CAPASSO ◽  
F. FLANDOLI
Keyword(s):  
Stochastic Model ◽  
Mean Field ◽  
Field Approximation ◽  
Angiogenic Factor ◽  
Mean Field Approximation ◽  
Time Interval ◽  
Biomedical Problem ◽  
The Family ◽  
The Mean ◽  
Points Of View

In the field of Life Sciences, it is very common to deal with extremely complex systems, from both analytical and computational points of view, due to the unavoidable coupling of different interacting structures. As an example, angiogenesis has revealed to be an highly complex, and extremely interesting biomedical problem, due to the strong coupling between the kinetic parameters of the relevant branching – growth – anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting underlying biochemical fields, at the macroscale. In this paper, an original revisited conceptual stochastic model of tumour-driven angiogenesis has been proposed, for which it has been shown that it is possible to reduce complexity by taking advantage of the intrinsic multiscale structure of the system; one may keep the stochasticity of the dynamics of the vessel tips at their natural microscale, whereas the dynamics of the underlying fields is given by a deterministic mean field approximation obtained by an averaging at a suitable mesoscale. While in previous papers, only an heuristic justification of this approach had been offered; in this paper, a rigorous proof is given of the so called ‘propagation of chaos’, which leads to a mean field approximation of the stochastic relevant measures associated with the vessel dynamics, and consequently of the underlying tumour angiogenic factor (TAF) field. As a side, though important result, the non-extinction of the random process of tips has been proven during any finite time interval.

scholarly journals Acceleration in turbulent channel flow: universalities in statistics, subgrid stochastic models and an application

2013 ◽  
Vol 721 ◽  
pp. 627-668 ◽  
Author(s):  
Rémi Zamansky ◽  
Ivana Vinkovic ◽  
Mikhael Gorokhovski
Keyword(s):  
Stochastic Model ◽  
Channel Flow ◽  
Scaling Law ◽  
Stochastic Modelling ◽  
Turbulent Channel Flow ◽  
Mean Value ◽  
Mean Velocity ◽  
Wall Distance ◽  
Eddy Simulation ◽  
The Mean

AbstractThis paper focuses on the characterization and the stochastic modelling of the fluid acceleration in turbulent channel flow. In the first part, the acceleration is studied by direct numerical simulation (DNS) at three Reynolds numbers (${\mathit{Re}}_{\ast } = {u}_{\ast } h/ \nu = 180$, 590 and 1000). It is observed that whatever the wall distance is, the norm of acceleration is log-normally distributed and that the variance of the norm is very close to its mean value. It is also observed that from the wall to the centreline of the channel, the orientation of acceleration relaxes statistically towards isotropy. On the basis of dimensional analysis, a universal scaling law for the acceleration norm is proposed. In the second part, in the framework of the norm/orientation decomposition, a stochastic model of the acceleration is introduced. The stochastic model for the norm is based on fragmentation process which evolves across the channel with the wall distance. Simultaneously the orientation is simulated by a random walk on the surface of a unit sphere. The process is generated in such a way that the mean components of the orientation vector are equal to zero, whereas with increasing wall distance, all directions become equally probable. In the third part, the models are assessed in the framework of large-eddy simulation with stochastic subgrid acceleration model (LES–SSAM), introduced recently by Sabel’nikov, Chtab-Desportes & Gorokhovski (Euro. Phys. J. B, vol. 80, 2011, p. 177–187), and designed to account for the intermittency at subgrid scales. Computations by LES–SSAM and its assessment using DNS data show that the prediction of important statistics to characterize the flow, such as the mean velocity, the energy spectra at small scales, the viscous and turbulent stresses, the distribution of the acceleration can be considerably improved in comparison with standard LES. In the last part of this paper, the advantage of LES–SSAM in accounting for the subgrid flow structure is demonstrated in simulation of particle-laden turbulent channel flows. Compared to standard LES, it is shown that for different Stokes numbers, the particle dynamics and the turbophoresis effect can be predicted significantly better when LES–SSAM is applied.

INTEGRATION OF IMPERFECT DEBUGGING IN GENERAL TESTING-DOMAIN DEPENDENT NHPP SRGM

2005 ◽  
Vol 12 (06) ◽  
pp. 493-505 ◽  
Author(s):  
JOONG-YANG PARK ◽  
YANG-SOOK HWANG ◽  
TAKAJI FUJIWARA
Keyword(s):  
Value Function ◽  
Reduction Rate ◽  
Mean Value ◽  
Value Functions ◽  
Testing Strategy ◽  
Imperfect Debugging ◽  
Empirical Performance ◽  
Rate Functions ◽  
The Mean ◽  
Constant Fault

Recently the general testing-domain dependent NHPP SRGM is developed to reflect repeated execution of constructs and location of detected faults. It assumes that debugging is perfect. Since realistic models need to reflect imperfect debugging, this paper integrates imperfect debugging in the general testing-domain dependent NHPP SRGM. Differential equations representing the mean value function are first derived for general testing strategy and then realized for the uniform testing. Specific mean value functions are obtained for some selected fault detection rate functions and constant fault reduction rate. Finally empirical performance evaluation is fulfilled.

AVERAGE NUMBER OF EVENTS AND AVERAGE REWARD

2000 ◽  
Vol 14 (4) ◽  
pp. 485-510
Author(s):  
Jie Mi
Keyword(s):  
Renewal Process ◽  
Finite Time ◽  
Counting Process ◽  
Interarrival Time ◽  
Time Interval ◽  
Average Reward ◽  
Finite Time Interval ◽  
Reward Process ◽  
The Mean ◽  
Renewal Reward Process

In a renewal process, the interarrival times are independent and identically distributed, and in a renewal reward process, the pairs of reward and interarrival time are i.i.d. Many useful results hold for these processes. This paper relaxes the assumption of identical distributions while keeping the assumption of independence. This paper explores the properties of the mean average number of occurrence of events and the mean average reward on any finite time interval. The paper also discusses the limiting properties of these two quantities and extends many results from the renewal process and renewal reward process to the more general counting process and reward sequence.

An application of the minimum discrimination information estimate to compute log-likelihood ratios

1973 ◽  
Vol 10 (2) ◽  
pp. 469-474
Author(s):  
E. L. Melnick ◽  
S. Kullback
Keyword(s):  
Continuous Time ◽  
Value Function ◽  
Mean Value ◽  
The Other ◽  
Likelihood Ratios ◽  
Log Likelihood ◽  
Discrimination Information ◽  
The Mean ◽  
Nikodym Derivative ◽  
Minimum Discrimination Information

In this paper the minimum discrimination information estimate is used to compute the log-likelihood ratio or logarithm of the Radon-Nikodym derivative In (dP1/dP2) when the stochastic process {x(t), t∈T) has either the probability measure P1 or P2. One example tests the mean value function of Gaussian processes. The other tests the mean value function of a continuous time Poisson process.

Closure and Monotonicity Properties of Nonhomogeneous Poisson Processes and Record Values

1988 ◽  
Vol 2 (4) ◽  
pp. 475-484 ◽  
Author(s):  
Ramesh C. Gupta ◽  
S.N.U.A. Kirmani
Keyword(s):  
Value Function ◽  
Record Values ◽  
Mean Value ◽  
Poisson Processes ◽  
Minimal Repair ◽  
Nonhomogeneous Poisson Processes ◽  
Upper Record Values ◽  
The Mean ◽  
Upper Record ◽  
Occurrence Times

Interconnections between occurrence times of nonhomogeneous Poisson processes, record values, minimal repair times, and the relevation transform are explained. A number of properties of the distributions of occurrence times and interoccurrence times of a nonhomogeneous Poisson process are proved when the mean-value function of the process is convex, starshaped, or superadditive. The same results hold for upper record values of independently identically distributed random variables from IFR, IFRA, and NBU distributions.

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