arXiv subjects
Publications and source records attributed to C. Phonsom.
Parabolic integro-differential nondegenerate Cauchy problem is considered in the scale of L_{p} spaces of functions whose regularity is defined by a Levy measure with O-regulary varying radial profile. Existence and uniqueness of a solution is proved by deriving apriori estimates. Some probability density function estimates of the associated Levy process are used as well.
Stochastic parabolic integro-differential problem is considered in the whole space. By verifying Hörmander condition, the existence and uniqueness is proved in Lp-spaces of functions whose regularity is defined by a scalable Levy measure. Some rough probability density function estimates of the associated Levy process are used as well.
Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniqueness of a solution is proved by deriving apriori estimates. Some rough probability density function estimates of the associated Levy process are used as well.
Elliptic and parabolic integro-differential model problems are considered in the whole space. By verifying Hörmander condition, the existence and uniqueness is proved in L_{p}-spaces of functions whose regularity is defined by a scalable, possibly nonsymmetric, Levy measure. Some rough probability density function estimates of the associated Levy process are used as well.