Fractional Poisson process: long-range dependence and applications in ruin theory

Renewal process, fractional Poisson process and distribution, fractional Kolmogorov-Feller equation, continuous time random walk, generalized fractional diffusion.. ∗

The fractional Poisson field (fPf) can be interpreted in term of the number of balls falling down on each point of R D , when the centers and the radii of the balls are thrown at

Keywords: compound Poisson model, ultimate ruin probability, natural exponential fam- ilies with quadratic variance functions, orthogonal polynomials, gamma series expansion,

The mean of the absolute values of the forecasting errors obtained with this estimator is approximately equal to 771 ft 3 /s, and the forecast of the flow on the next day is better,

This section is dedicated to numerical illustrations of the theoretical results regarding some exact and asymptotic expressions of the mean, variance, covariance and correlation of

Keywords Ruin probabilities · Dual models · Price process · Renewal theory · Distribu- tional equation · Autoregression with random coefficients · L´evy process.. Mathematics

Asymptotic multivariate finite-time ruin probabilities with heavy- tailed claim amounts: Impact of dependence and optimal reserve allo- cation.. ROMAIN

The fractional Poisson field (fPf) is constructed by considering the number of balls falling down on each point of R D , when the centers and the radii of the balls are thrown at