Bernoulli

  • Bernoulli
  • Volume 19, Number 5B (2013), 2455-2493.

Diffusions with rank-based characteristics and values in the nonnegative quadrant

Tomoyuki Ichiba, Ioannis Karatzas, and Vilmos Prokaj

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Abstract

We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according to rank; one of the variances is allowed to vanish, but not both. The construction involves solving a system of coupled Skorokhod reflection equations, then “unfolding” the Skorokhod reflection of a suitable semimartingale in the manner of Prokaj (Statist. Probab. Lett. 79 (2009) 534–536). Questions of pathwise uniqueness and strength are also addressed, for systems of stochastic differential equations with reflection that realize these diffusions. When the variance of the laggard is at least as large as that of the leader, it is shown that the corner of the quadrant is never visited.

Article information

Source
Bernoulli Volume 19, Number 5B (2013), 2455-2493.

Dates
First available in Project Euclid: 3 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1386078610

Digital Object Identifier
doi:10.3150/12-BEJ459

Mathematical Reviews number (MathSciNet)
MR3160561

Zentralblatt MATH identifier
1286.60077

Keywords
diffusion with reflection and rank-dependent characteristics semimartingale local time skew representations Skorokhod problem sum-of-exponential stationary densities Tanaka formula and equation unfolding nonnegative semimartingales weak and strong solutions

Citation

Ichiba, Tomoyuki; Karatzas, Ioannis; Prokaj, Vilmos. Diffusions with rank-based characteristics and values in the nonnegative quadrant. Bernoulli 19 (2013), no. 5B, 2455--2493. doi:10.3150/12-BEJ459. https://projecteuclid.org/euclid.bj/1386078610


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