1,721,118 research outputs found
Large deviations for compound Markov renewal processes with dependent jump sizes and jump waiting times
No full textIn [17] the author considered a compound Markov renewal process ((S) over tilde (Nt)) where ((J(n), S-n)) and (((J) over tilde (n), (S) over tilde (n))) are suitable independent Markov additive processes such that (S-n - Sn-1) are positive random variables, and N-t = Sigma(n >= 1) > 1(Sn <= t). In this paper we present the analogous results for a more general situation where we consider a unique Markov additive process ((J(n), Z(n))) in place of ((J(n), S-n)) and (((J) over tilde (n), (S) over tilde (n)))and Z(n) = ((S) over tilde (n), S-n). Some further results are also presented; in particular we relate in terms of large deviations the sequence (((S) over tilde (n), S-n)) and the process (((S) over tilde (Nt), N-t))
Large deviation results for compound Markov renewal processes
No full textIn this paper we present some large deviation results for compound Markov renewal processes. We start studying the exponential decay of level crossing probabilities as the level goes to infinity. Furthermore we consider a technique called importance sampling to estimate a level crossing probability by Monte Carlo simulations when the level is large; in particular we find an asymptotically efficient simulation law according to a
sense specified in other works on the same topic
The equivalence between "domination of a Bayesian experiment" and "a.e. domination of a statistical structure": the role of the predictive probability
No full textLarge deviations for Bayesian estimators in first-order autoregressive processes
No full textIn this paper we consider first-order autoregressive processes and we allow either
centered Normal or exponential innovations. We prove large deviation principles for
posterior distributions on the unknown parameter and, motivated by potential
applications in risk theory, we also prove large deviation principles for Bayesian
estimators of Lundberg’s parameter
Large deviations for some normalized sums of exponentially distributed random variables
No full textWe prove large deviation results for sequences of normalized sums which
are defined in terms of triangular arrays of exponentially distributed random
variables. We also present some examples: one of them might have applications
in reliability theory because it concerns the spacings of i.i.d. exponentially
distributed random variables; in another one we consider a sequence of
logarithmically weighted means
Mixed parametrization for curved exponential models in homogeneous Markov processes with a finite state space
No full textLarge deviations for risk models in which each main claim induces a delayed claim
Full text linkIn reality insurance claims may be delayed for several reasons and risk models with this feature have been discussed for some years. In this paper we present a sample path large deviation principle for the delayed claims risk model presented in
(Yuen K.C., Guo J., and Ng K.W., 2005, On ultimate ruin in a delayedclaims
model, Journal of Applied Probability, 42, 163 – 174). Roughly speaking each main
claim induces another type of claim called by-claim; any by-claim occurs later than its main claim and the time of delay is random. Successively we use Ga¨rtner Ellis Theorem to prove a large deviation principle for a more general version of this model, in which the following items depend on the evolution of an irreducible(continuous time) Markov chain with finite state space: the intensity of the Poisson claim number process,
the distribution of the claim sizes and the distribution of the random times of delay. Finally we present the Lundberg’s estimate for the ruin probabilities; in the fashion of large deviations this estimate provides the exponential decay of the ruin probability as the initial capital goes to infinity
Large deviations for the time-integrated negative parts of some processes
No full textIn this paper we consider a family of processes which satisfies the large deviation principle with a good rate function; then we prove the large deviation principle for the family of the corresponding time-integrated negative parts, with the application of the so-called contraction principle. An explicit expression of the rate function is presented for a class of examples
Large deviations for some non-standard telegraph processes
No full textWe prove large deviation principles for three non-standard telegraph processes. The first
one is a damped model with velocity driven by Bernoulli trials studied in Crimaldi et al.
(2013), and we obtain the same rate function obtained in De Gregorio and Macci (2014) for
another damped telegraph process. The other telegraph processes are non-damped models
and we assume suitable hypotheses: in a case the holding times have a general superexponential
distribution, in another case the change-of-direction number process satisfies
a large deviation principl
- …
