Consider a simple random walk on ℤ with coloring of ℤ. Look at the sequence first N steps taken in walk, together colors visited locations. We call this record. From record one can deduce interval that was visited, which is size approximately $$\sqrt $$ . This called scenery reconstruction. Now suppose an adversary may change δN entries obtained. What we from about now? In paper show it likely ...

This thesis aim is to present results on a stochastic model called reinforced random walk. This process was conceived in the late 1980’s by Coppersmith and Diaconis and can be regarded as a generalization of a random walk on a weighted graph. These reinforced walks have non-homogeneous transition probabilities, which arise from an interaction between the process and the weights. We survey artic...

This note presents a proof of Pólya’s random walk theorem using classical methods from special function theory and asymptotic analysis.

We present the method of the quasi-random walk for the approximation of functionals of the solution of second kind Fredholm integral equations. This deterministic approach efficiently uses low discrepancy sequences for the quasi-Monte Carlo integration of the Neumann series. The fast procedure is illustrated in the setting of computer graphics, where it is applied to several aspects of the glob...

This paper considers a class of non-Markovian discrete-time random processes on a finite state space {1, . . . , d}. The transition probabilities at each time are influenced by the number of times each state has been visited and by a fixed a priori likelihood matrix, R, which is real, symmetric and nonnegative. Let Si(n) keep track of the number of visits to state i up to time n, and form the f...

financial scientists have always been eager to distinguish between whether the price series could be random walk (unit root) or mean reverting processes.by a random walk we mean that accruing shocks to the system have permanent impacts and prices do not revert to their previous trend path, in addition, regarding to random walk processes the price series volatility could increase with out any li...