Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...

‎In this paper we establish a new numerical method for solving a class of stochastic partial differential equations (SPDEs) based on B-splines wavelets‎. ‎The method combines implicit collocation with the multi-scale method‎. Using the multi-scale method‎, ‎SPDEs can be solved on a given subdomain with more accuracy and lower computational cost than the rest of the domain‎. ‎The stability and c...

Stochastic partial differential equations arise as mathematical models of complex multiscale systems under random influences. Invariant manifolds often provide geometric structure for understanding stochastic dynamics. In this paper, a random invariant manifold reduction principle is proved for a class of stochastic partial differential equations. The dynamical behavior is shown to be described...