| Abstract: |
| We consider the Cauchy problem for a linear stochastic partial differential equation. By extending
the parametrix method for PDEs whose coefficients are only measurable with respect to the time
variable, we prove existence, regularity in H\older classes and estimates from above and below of
the fundamental solution. This result is applied to SPDEs by means of the It\^o-Wentzell formula,
through a random change of variables which transforms the SPDE into a PDE with random
coefficients. |
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