2025-03-262025-03-2613-07-2016https://pyxida.aueb.gr/handle/123456789/7370The first part of this thesis studies forward and backward versions of the random Burgers equation (RBE) with stochastic coeffcients. First, the celebrated Cole-Hopf transformation reduces the forward RBE to a forward random heat equation (RHE) that can be treated pathwise. Next we provide a connection between the backward Burgers equation and a system of forward backward stochastic differential equations (FBSDEs). Exploiting this connection, we derive a generalization of the Cole-Hopf transformation which links the backward RBE with the backward RHE and investigate the range of its applicability. Stochastic Feynman- Kac representations for the solutions are provided. Explicit solutions are constructed and applications to stochastic control and mathematical finance are discussed.164p.CC BY: Attribution alone 4.0https://creativecommons.org/licenses/by/4.0/Stochastic Differential Equations (BSDEs)Random burgers equation(In-)Finite horizon random (FBSDE)Text