Limit theorems and governing equations for Lévy walks
نویسندگان
چکیده
منابع مشابه
Fractional governing equations for coupled random walks
Keywords: Fractional calculus Anomalous diffusion Continuous time random walk Central limit theory Operator stable law a b s t r a c t In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW is coupled if the waiting time and the subsequent jump are dependent random variables. The CTRW is used in physics to model diffusing particles. Its scaling limit ...
متن کاملLimit Theorems for Random Walks with Boundaries
In this review, we consider boundary problems for random walks generated by sums of independent items and some of their generalizations. Let 1, 42, . . * be identically distributed independent random variables with distribution frunction F(x). Let S = 0, Sn = Sk= Ok with n = 1, 2, * -. We shall study the properties of the random trajectory formed by the sums S0, S1, 82, . Let n be an integer pa...
متن کاملConditional limit theorems for ordered random walks
In a recent paper of Eichelsbacher and König (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a k-dimensional random walk conditioned to stay in a strict order at all times. Moreover, they have shown that the rescaled random walk converges to the Dyson Brownian motion. In the present paper we find the ...
متن کاملThe Euler Scheme for Lévy Driven Stochastic Differential Equations : Limit Theorems
We study the Euler scheme for a stochastic differential equation driven by a Lévy process Y . More precisely, we look at the asymptotic behavior of the normalized error process un(X −X), where X is the true solution and X is its Euler approximation with stepsize 1/n, and un is an appropriate rate going to infinity: if the normalized error processes converge, or are at least tight, we say that t...
متن کاملExcursions and local limit theorems for Bessel - like random walks ∗
We consider reflecting random walks on the nonnegative integers with drift of order 1/x at height x . We establish explicit asymptotics for various probabilities associated to such walks, including the distribution of the hitting time of 0 and first return time to 0, and the probability of being at a given height k at time n (uniformly in a large range of k.) In particular, for drift of form −δ...
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: Stochastic Processes and their Applications
سال: 2015
ISSN: 0304-4149
DOI: 10.1016/j.spa.2015.05.014