PERTURBATION OF AN α-STABLE STOCHASTIC PROCESS AND THE FUNDAMENTAL SOLUTION OF A CERTAIN PARABOLIC PSEUDODIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS - Hutsuliak, Yu. V.; Osypchuk, M. M. (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2025)
Using the method of perturbation of a rotationally invariant alpha-stable stochastic process, an explicit representation of the fundamental solution of the pseudodifferential equation \(tu(t,x)=-c(-Δ)^α/2u(t,·)(x)+ (a, abla_β u(t,·)(x)), t>0, xR^d\), where \(Δ\) is the Laplace operator, \( abla_β\) is the "pseudogradient" operator of order \(0<β<α\) (given by the symbol \(i|λ|^β-1λ\)). The case of fixed \(0<α<2,\) \(c>0\) and constant \(aR^d\) is considered.