Exit identities for Lévy processes observed at Poisson arrival times
نویسندگان
چکیده
منابع مشابه
An EM Algorithm for Markovian Arrival Processes Observed at Discrete Times
The present paper contains a specification of the EM algorithm in order to fit an empirical counting process, observed at discrete times, to a Markovian arrival process. The given data are the numbers of observed events in disjoint time intervals. The underlying phase process is not observable. An exact numerical procedure to compute the E and M steps is given.
متن کاملOptimal first-arrival times in Lévy flights with resetting.
We consider the diffusive motion of a particle performing a random walk with Lévy distributed jump lengths and subject to a resetting mechanism, bringing the walker to an initial position at uniformly distributed times. In the limit of an infinite number of steps and for long times, the process converges to superdiffusive motion with replenishment. We derive a formula for the mean first arrival...
متن کاملParametric Estimation of Diffusion Processes Sampled at First Exit Times
This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and asymptotic normality of an appropriate normalization are proved. The results are applied to two examples from the financial literature; viz., Cox-Ingersoll-Ross’ mod...
متن کاملNonparametric adaptive estimation for discretely observed Lévy processes
This thesis deals with nonparametric estimation methods for discretely observed Lévy processes. The following statistical framework is considered: A Lévy process X having finite variation on compact sets and finite second moments is observed at low frequency. In this situation, the jump dynamics is fully described by the finite signed measure μ(dx) = xν(dy). The goal is to estimate, nonparametr...
متن کاملOn first exit times for homogeneous diffusion processes
Here t ≥ 0, wt is a standard d-dimensional Wiener process, coordinated as usual with some rightcontinuous non-decreasing flow of σ-algebras Ft ⊂ F ; fi and βi are nonrandom functions with respective values in R and R, (here and elsewhere i = 1, 2). The random vectors ai are measurable with respect to the σ-algebra F0 and ai ∈ Q̄ with probability 1(Q̄ denotes the closure of the region Q ). All vec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bernoulli
سال: 2016
ISSN: 1350-7265
DOI: 10.3150/15-bej695