The class of pseudoaffine (or more general ‘triangular’) Rn → Rn (n≤2) transformations, used in our previous works in the process of constructing n-variate pdfs (such as, for example, pseudonormal), is extended, as n → ∞, to infinite dimensional spaces. This transition opens the way for construction of many new stochastic processes with discrete time. As a next step, a transition to continuous time processes enriches the underlying theory. The so obtained stochastic processes reveal interesting analytic properties. Some of the newly obtained processes are Markovian or k–th order Markovian. As a central result, a Wiener process is obtained along with its new generalization. A subclass of the so obtained class of extended Wiener stochastic processes is shown also to be alternatively described by a corresponding class of parabolic form partial differential equations with variable coefficients. That class of differential equations is an extension of the well-known class of Einstein parabolic differential equations related to the original Wiener process. There is a one-to-one correspondence between each particular extended wiener process belonging to the defined process subclass, and related extended Einstein partial differential equation.