Tanaka formula for strictly stable processes
نویسندگان
چکیده
منابع مشابه
Brownian motion, reflection groups and Tanaka formula
In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka’s formula for linear Brownian motion. The paper is closed with a description of the boun...
متن کاملBasic Potential Theory of Certain Nonsymmetric Strictly Α-stable Processes
We study potential theoretic properties of strictly α-stable processes whose Lévy measure is comparable to that of a symmetric αstable process. We show the existence, continuity and strict positivity of transition densities and Green function of the process killed upon exiting a bounded domain. We further show that the exit distributions of the process from a domain satisfying the uniform volum...
متن کاملEstimation for Strictly Positive Stable Laws
Positive stable laws have become a standard tool in modelling heavy tailed data in such diverse areas as finance, engineering and survival analysis. Due to the non–existence of closed–form expression for the corresponding densities, standard procedures for estimation of the parameters of positive stable distributions appear to be computationally expensive. In this note we show that the first tw...
متن کاملA Tanaka formula for the derivative of intersection local time in R 1
Abstract Let Bt be a one dimensional Brownian motion, and let α ′ denote the derivative of the intersection local time of Bt as defined in [3]. The object of this paper is to prove the following formula 1 2 αt(x) + 1 2 sgn(x)t = ∫ t 0 LBs−x s dBs − ∫ t 0 sgn(Bt −Bu − x)du (0.1) which was given as a formal identity in [3] without proof. Let B denote Brownian motion in R. In [3], Rosen demonstrat...
متن کاملStrictly Increasing Markov Chains as Wear Processes
To model the lifetime of a device, increasing Markov chains are used. The transition probabilities of the chain are as follows: pi, j = p if j = i+δ, and pi, j = 1− p if j = i+2δ. The mean time to failure of the device, namely the mean number of transitions required for the process, starting from x0, to take on a value greater than or equal to x0 + kδ is computed explicitly. A second version of...
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: Probability and Mathematical Statistics
سال: 2019
ISSN: 2300-8113,0208-4147
DOI: 10.19195/0208-4147.39.1.3