Asymptotic properties of Brownian motion delayed by inverse subordinators

By Marcin Magdziarz, René L. Schilling. 2013

71 citations recorded by the source corpus.

We study the asymptotic behaviour of the time-changed stochas- tic process f X(t) = B( f S(t)), where B is a standard one-dimensional Brow- nian motion and f S is the (generalized) inverse of a subordinator, i.e. the first-passage time process corresponding to an increasing Lprocess with Laplace exponent f. This type of processes plays an important role in statis- tical physics in the modeling of anomalous subdiffusive dynamics. The main result of the paper is the proof of the mixing property for the sequence of stationary increments of a subdiffusion process. We also investigate various martingale properties, derive a generalized Feynman-Kac formula, the laws of large numbers and of the iterated logarithm for f X.

Subfields: Finance, Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/9b98d4538b5b23bc46c7ebce16eaf43b36158729

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In Finance

1. Mark M. Meerschaert
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2. Mark M. Meerschaert
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In Modeling and Simulation

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Citations in the corpus

• Relaxation patterns and semi-Markov dynamics (2015, methodology): “A third approach was adopted in Magdziarz and Schilling [32]: the authors pointed out that the distribution (one-dimensional marginal) of B ( L f (t) ) , a special case of the CTRW scaling limit where B is a Brownian motion, is the fundamental solution to the generalized diffusion equation ∂ ∂t q(x,”