Representation of functionals of Ito processes and their first exit times
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The representation theorem is obtained for functionals of non-Markov processes and their first exit times from bounded domains. These functionals are represented via solutions of backward parabolic Ito equations. As an example of applications, analogs of forward Kolmogorov equations are derived for conditional probability density unctions of Ito processes killed on the boundary. In addition, a maximum principle and a contraction property are established for SPDEs in bounded domains.
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