Strong solutions of stochastic equations with rank-based coefficients

By Tomoyuki Ichiba, Ioannis Karatzas, Mykhaylo Shkolnikov. 2011

72 citations recorded by the source corpus.

We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We show that strong existence and uniqueness hold until the first time three particles collide. Motivated by this result, we improve significantly the existing conditions for the absence of such triple collisions in the case of finite-dimensional systems, and provide the first condition of this type for systems with a countable infinity of particles.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/81ca5f7126c8d4555dd7ef7b2e98816b42efc8e1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Mykhaylo Shkolnikov
2. Soumik Pal
3. Ioannis Karatzas
4. Tomoyuki Ichiba
5. Constantinos Kardaras
6. Gordan Zitkovic
7. Marcel Nutz
8. Philip Protter

In Management Science and Operations Research

1. Soumik Pal
2. Mykhaylo Shkolnikov
3. Ioannis Karatzas
4. Gordan Zitkovic
5. Constantinos Kardaras

In Mathematical Physics

1. Mykhaylo Shkolnikov
2. Ioannis Karatzas
3. Soumik Pal
4. Tomoyuki Ichiba

Citations in the corpus

• Systems of Brownian particles with asymmetric collisions (2012, background): “2 of [21], or as in the proof of Lemmata 6 and 7 in [22], we need only consider the case b1 = b2 = · · · = bn = 0 in (1.”