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Large-time and small-time behaviors of the spectral heat content for time-changed stable processes. (English) Zbl 1507.60064

Summary: We study the large-time and small-time asymptotic behaviors of the spectral heat content for time-changed stable processes, where the time change belongs to a large class of inverse subordinators. For the large-time behavior, the spectral heat content decays polynomially with the decay rate determined by the Laplace exponent of the underlying subordinator, which is in sharp contrast to the exponential decay observed in the case when the time change is a subordinator. On the other hand, the small-time behavior exhibits three different decay regimes, where the decay rate is determined by both the Laplace exponent and the index of the stable process.

MSC:

60G51 Processes with independent increments; Lévy processes
60G52 Stable stochastic processes
60K50 Anomalous diffusion models (subdiffusion, superdiffusion, continuous-time random walks, etc.)
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