  The P\'olya urn scheme is a discrete-time process concerning the addition and
removal of colored balls. There is a known embedding of it in continuous-time,
called the P\'olya process. We deal with a generalization of this stochastic
model, where the initial values and the entries of the transition matrix
(corresponding to additions or removals) are not necessarily fixed integer
values as in the standard P\'olya process. In one of the scenarios, we even
allow the entries of the matrix to be random variables. As a result, we no
longer have a combinatorial model of "balls in an urn," but a broader
interpretation as a random walk in a possibly high number of dimensions. In
this paper, we study several parametric classes of these generalized continuum
P\'olya-like random walks.
