a random walk on a lattice is one of the most fundamental models in probability theory. when the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (rwre). the basic questions such as the law of large numbers (lln), the central limit theorem (clt), and the large deviation principle (ldp) are no...

in the present paper, an algorithm is presented for reliability analysis of beams with random material properties under static spatially random loads. the randomness may be due to the employed manufacturing process that leads to components with slightly different microstructures. since the material properties are random, the stiffness matrices and subsequently, the response will be of random na...

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.