Spectral Analysis of a Class of Non-local Elliptic Operators Related to Brownian Motion with Random Jumps

@inproceedings{Pinsky2008SpectralAO,
  title={Spectral Analysis of a Class of Non-local Elliptic Operators Related to Brownian Motion with Random Jumps},
  author={Ross G. Pinsky},
  year={2008}
}
Let D ⊂ R be a bounded domain and let P(D) denote the space of probability measures on D. Consider a Brownian motion in D which is killed at the boundary and which, while alive, jumps instantaneously at an exponentially distributed random time with intensity γ > 0 to a new point, according to a distribution μ ∈ P(D). From this new point it repeats the above behavior independently of what has transpired previously. The generator of this process is an extension of the operator −Lγ,μ, defined by L… CONTINUE READING

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