Analytical expansions for parabolic equations
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q-fin.CP
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equationparabolicanalyticalapproximationsarbitrarilyassociatedasymptoticboot-strapping
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We consider the Cauchy problem associated with a general parabolic partial differential equation in $d$ dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as rigorous short-time error estimates. Using a boot-strapping technique, we also provide convergence results for arbitrarily large time intervals.
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