Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations
Christian Bender, Marie Bormann, Yana A. Butko
Abstract
Abstract We consider a class of generalized time-fractional evolution equations containing a fairly general memory kernel k and an operator L being the generator of a strongly continuous semigroup. We show that a subordination principle holds for such evolution equations and obtain Feynman-Kac formulae for solutions of these equations with the use of different stochastic processes, such as subordinate Markov processes and randomly scaled Gaussian processes. In particular, we obtain some Feynman-Kac formulae with generalized grey Brownian motion and other related self-similar processes with stationary increments.
Topics & Concepts
MathematicsSemigroupSubordination (linguistics)Feynman diagramFractional Brownian motionPropagatorBrownian motionMarkov processClass (philosophy)Kernel (algebra)Generator (circuit theory)Operator (biology)Mathematical physicsApplied mathematicsPure mathematicsMathematical analysisPhysicsQuantum mechanicsPower (physics)BiochemistryLinguisticsTranscription factorChemistryRepressorGenePhilosophyArtificial intelligenceComputer scienceStatisticsFractional Differential Equations SolutionsStochastic processes and financial applicationsNonlinear Differential Equations Analysis