Strong approximation of stochastic processes using random walks
نویسندگان
چکیده
منابع مشابه
ar X iv : m at h / 07 03 33 9 v 1 [ m at h . FA ] 1 2 M ar 2 00 7 APPROXIMATION OF QUANTUM LÉVY PROCESSES BY QUANTUM RANDOM WALKS
Every quantum Lévy process with a bounded stochastic generator is shown to arise as a strong limit of a family of suitably scaled quantum random walks. The note is concerned with investigating convergence of random walks on quantum groups to quantum Lévy processes. The theory of the latter is a natural non-commutative counterpart of the theory of classical Lévy processes on groups ([Hey]). It h...
متن کاملRandom-walk approximation to vacuum cocycles
Quantum random walks are constructed on operator spaces using the concept of matrix-space lifting, a form of ampliation intermediate between those given by spacial and ultraweak tensor products. It is shown that these walks, after suitable scaling, converge in a strong sense to vacuum cocycles, certain vacuum-adapted processes which are Feller cocycles in the sense of Lindsay and Wills. This re...
متن کاملStochastic Bounds for Lévy Processes
Using the Wiener–Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Lévy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Lévy process versions of many known results about the large-time behavior of random walks. This is illustrat...
متن کاملBranching Random Walks and Their Applications to Population Studies
Recent investigations have demonstrated that continuous-time branching random walks on multidimensional lattices give an important example of stochastic models in which the evolutionary processes depend on the structure of a medium and the spatial dynamics. It is convenient to describe such processes in terms of birth, death, and walks of particles on the lattice. The structure of a medium is d...
متن کاملLimit Theorem for Continuous-time Random Walks with Two Time Scales
Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics tomodel particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations t...
متن کامل