J o u r n a l o f P r o b a b i l i t y Electron. Abstract For normally reflected Brownian motion and for simple random walk on independently growing in time d-dimensional domains, d ≥ 3, we establish a sharp criterion for recurrence versus transience in terms of the growth rate.
We consider recurrence versus transience for models of random walks on growing in time, connected subsets Gt of some fixed locally finite, connected graph, in which monotone interaction enforces such growth as a result of visits by the walk (or probes it sent), to the neighborhood of the boundary of Gt.
An algorithm for solving continuous-time stochastic optimal control problems is presented. The numerical scheme is based on the stochastic maximum principle (SMP) as an alternative to the widely studied dynamic programming principle (DDP). By using the SMP, (Peng, 1990) obtained a system of coupled forward-backward stochastic differential equations (FBSDE)… (More)