Compositions of random functions on a finite set.
Compound Compound Poisson Risk Model
2000 Mathematics Subject Classification: 60K10, 62P05.The compound Poisson risk models are widely used in practice. In this paper the counting process in the insurance risk model is a compound Poisson process. The model is called Compound Compound Poisson Risk Model. Some basic properties and ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular case of the Pólya-Aeppli...
Compound Poisson approximation for extremes of moving minima in arrays of independent random variables
We present conditions sufficient for the weak convergence to a compound Poisson distribution of the distributions of the kth order statistics for extremes of moving minima in arrays of independent random variables.
Compound Poisson approximation of word counts in DNA sequences
Compound Poisson approximation of word counts in DNA sequences
Identifying words with unexpected frequencies is an important problem in the analysis of long DNA sequences. To solve it, we need an approximation of the distribution of the number of occurrences N(W) of a word W. Modeling DNA sequences with m-order Markov chains, we use the Chen-Stein method to obtain Poisson approximations for two different counts. We approximate the “declumped” count of W by a Poisson variable and the number of occurrences N(W) by a compound Poisson variable. Combinatorial...
Computation of Greeks for barrier and look-back options using Malliavin calculus.
Computation of Greeks using Malliavin's calculus in jump type market models.
Computation of moments for the length of the one dimensional ISE support.
Computation of the limiting distribution in queueing systems with repeated attempts and disasters
Computation of the limiting distribution in queueing systems with repeated attempts and disasters
Single server queues with repeated attempts are useful in the modeling of computer and telecommunication systems. In addition, we consider in this paper the possibility of disasters. When a disaster occurs, all the customers present in the system are destroyed immediately. Using a regenerative approach, we derive a numerically stable recursion scheme for the state probabilities. This model can be employed to analyze the behaviour of a buffer in computers with virus infections.
Computational fluctuating fluid dynamics
This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret...
Computational procedures for a class of GI/D/ systems in discrete time.
Computational schemes for two exponential servers where the first has a finite buffer
We consider a system consisting of two not necessarily identical exponential servers having a common Poisson arrival process. Upon arrival, customers inspect the first queue and join it if it is shorter than some threshold n. Otherwise, they join the second queue. This model was dealt with, among others, by Altman et al. [Stochastic Models20 (2004) 149–172]. We first derive an explicit expression for the Laplace-Stieltjes transform of the distribution underlying the arrival (renewal) process to...
Computational schemes for two exponential servers where the first has a finite buffer
We consider a system consisting of two not necessarily identical exponential servers having a common Poisson arrival process. Upon arrival, customers inspect the first queue and join it if it is shorter than some threshold n. Otherwise, they join the second queue. This model was dealt with, among others, by Altman et al. [Stochastic Models20 (2004) 149–172]. We first derive an explicit expression for the Laplace-Stieltjes transform of the distribution underlying the arrival (renewal) process to...
Computer simulation of a nonlinear model for electrical circuits with α-stable noise
The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to nonlinear 2nd order stochastic differential equations modeling some engineering systems subject to large random external disturbances. This provides us with quantitative results on their asymptotic behavior.
Computer-aided modeling and simulation of electrical circuits with α-stable noise
The aim of this paper is to demonstrate how the appropriate numerical, statistical and computer techniques can be successfully applied to the construction of approximate solutions of stochastic differential equations modeling some engineering systems subject to large disturbances. In particular, the evolution in time of densities of stochastic processes solving such problems is discussed.
Computing the Bounds on the Loss Rates
Computing the expectation of the Azéma-Yor stopping times
Computing the reliability of systems with statistical dependent elements.
Computing the Stackelberg/Nash equilibria using the extraproximal method: Convergence analysis and implementation details for Markov chains games
In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov's regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the...