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...

We consider branching random walk in environment (BRWRE) and prove the existence of deterministic subsequences along which their maximum, centered at its mean, is tight. This partially answers an open question arXiv:1711.00852. The method proof adapts argument developed by Dekking Host for walks with bounded increments. tightness without need remains open.