Stochastic equations, flows and measure-valued processes

By Donald A. Dawson, Zenghu Li. 2010

185 citations recorded by the source corpus.

We first prove some general results on pathwise uniqueness, comparison property and existence of nonnegative strong solutions of stochastic equations driven by white noises and Poisson random measures. The results are then used to prove the strong existence of two classes of stochastic flows associated with coalescents with multiple collisions, that is, generalized Fleming--Viot flows and flows of continuous-state branching processes with immigration. One of them unifies the different treatments of three kinds of flows in Bertoin and Le Gall [Ann. Inst. H. Poincar\'{e} Probab. Statist. 41 (2005) 307--333]. Two scaling limit theorems for the generalized Fleming--Viot flows are proved, which lead to sub-critical branching immigration superprocesses. From those theorems we derive easily a generalization of the limit theorem for finite point motions of the flows in Bertoin and Le Gall [Illinois J. Math. 50 (2006) 147--181].

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/33638825c51bac8c337f36f0a11905bf2b2f2cd9

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. Chunhua Ma
2. Zenghu Li
3. Fei Pu

In Mathematical Physics

1. Chunhua Ma
2. Zenghu Li
3. Fei Pu
4. Amaury Lambert
5. Gyula Pap
6. Mátyás Barczy
7. Martin Keller‐Ressel

In Statistics and Probability

1. Chunhua Ma
2. Zenghu Li
3. Fei Pu
4. Amaury Lambert
5. Martin Keller‐Ressel

Citations in the corpus

• Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model (2013, methodology): “By Theorem 3.2 of Dawson and Li (2012), we have P{Yt(x) ≥ Yt(y) ≥ 0 for all t ≥ 0} = 1 and {Yt(x) − Yt(y) : t ≥ 0} is a CB-process with branching mechanism φ; see also Remark 2.1 (iv) of Li and Ma (2008).”
• Continuous-State Branching Processes with Immigration (2019, methodology): “Their results were extended to flows of CBI-processes in Dawson and Li (2012) using strong solutions; see also Li (2014) and Li and Ma (2008).”
• Strong solutions of jump-type stochastic equations (2012, background): “The pathwise uniqueness for the equation follows from a result in [7].”