In this paper, a Banach space framework is introduced in order to deal with finite-dimensional path-dependent stochastic differential equations. A version of Kolmogorov backward equation is formulated ...

Mathematicians have found solutions to a 140-year-old, 7-dimensional equation that were not known to exist for more than a century despite its widespread use in modeling the behavior of gases.

Green's functions and propagators for the multi-dimensional anisotropic space-time fractional diffusion equation are obtained in integral form. Uniqueness of the solutions is studied in the framework ...