On Solutions of First Order Stochastic Partial Differential Equations

Details On Solutions of First Order Stochastic Partial Differential Equations On Solutions of First Order Stochastic Partial Differential Equations

2005-10-24

arxiv.org/abs/math/0510495v1

Mathematics

Probability

Scientific paper

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 $\pd Ut = DW$, and $\pd Ut-\pd Ux= DW$, where $D$ is a differential operator and $W(t,x)$ 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.

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