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On the Cauchy problem for parabolic integro-differential equations with space-dependent coefficients in generalized H\"{o}lder classes. (arXiv:1810.00677v1 [math.PR])

来源于:arXiv
Parabolic integro-differential Kolmogorov equations with space-dependent coefficients are considered in H\"{o}lder-type spaces defined by a scalable L\'{e}vy measure. Probabilistic representations are used to prove continuity of the operator. Existence and uniqueness of the solution are established and some regularity estimates are obtained. 查看全文>>