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Local martingales with two reflecting barriers

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Author

Summary, in English

We give an account of the characteristics that result from reflecting a drifting local martingale (i.e. the sum of a local martingale and a multiple of its quadratic variation process) in 0 and b > 0. We present conditions which guarantee the existence of finite moments of what is required to keep the reflected process within its boundaries. Also, we derive an associated law of large numbers and a central limit theorem which apply when the input is continuous. Similar results for integrals of the paths of the reflected process are also presented. These results are in close agreement to what has previously been shown for Brownian motion.

Department/s

Publishing year

2015

Language

English

Pages

1062-1075

Publication/Series

Journal of Applied Probability

Volume

52

Issue

4

Document type

Journal article

Publisher

Applied Probability Trust

Topic

  • Probability Theory and Statistics

Keywords

  • Skorokhod problem
  • reflection
  • stochastic integration
  • Brownian motion
  • local martingale
  • semimartingale

Status

Published

Research group

  • Geriatrics
  • Geriatric Medicine

ISBN/ISSN/Other

  • ISSN: 1475-6072