Abstract: This note is concerned with an important for modelling
question of existence of solutions of stochastic partial differential equations
as proper stochastic processes, rather than processes in the generalized sense.
We consider a first order stochastic partial differential equations of the form and where D
is a differential operator and is a continuous but
non-differentiable function (field). We give a necessary and sufficient
condition for stochastic equations to have solutions as functions. The result is
then applied
to the equation for a yield curve. Proofs are based on probability arguments.
Keywords and phrases: first order stochastic partial differential equations.
