Aging uncoupled continuous time random walk limits
نویسندگان
چکیده
منابع مشابه
Stochastic calculus for uncoupled continuous-time random walks.
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingal...
متن کاملContinuous time ‘ true ’ self - avoiding random walk on Z
We consider the continuous time version of the 'true' or 'myopic' self-avoiding random walk with site repulsion in 1d. The Ray – Knight-type method which was applied in [15] to the discrete time and edge repulsion case, is applicable to this model with some modifications. We present a limit theorem for the local time of the walk and a local limit theorem for the displacement.
متن کاملExtremal behavior of a coupled continuous time random walk
Coupled continuous time random walks (CTRW) model normal and anomalous diffusion of random walkers by taking the sum of random jump lengths dependent on the random waiting times immediately preceding each jump. They are used to simulate diffusion-like processes in econophysics such as stock market fluctuations, where jumps represent financial market microstructure like log-returns. In this and ...
متن کاملContinuous time random walk and parametric subordination in fractional diffusion
The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW) is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW itself. We treat the CTRW as a combination of a random walk on the axis of physical time with a random walk in space, both walks happening in discrete oper...
متن کاملDephasing by a continuous-time random walk process.
Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions such as (exp(i ∫(0)(t) Q(s)ds)), where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets denote ensemble averaging. This paper gives an exact evaluation of these functions for the case where Q is a continuous-time random walk process. The cont...
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: Electronic Journal of Probability
سال: 2016
ISSN: 1083-6489
DOI: 10.1214/16-ejp3802