Degenerate stochastic differential equations arising from catalytic branching networks
| dc.creator | Bass, Richard F. | |
| dc.creator | Perkins, Edwin A. | |
| dc.date | 2008-01-21 | |
| dc.date.accessioned | 2026-07-07T08:55:41Z | |
| dc.date.available | 2026-07-07T08:55:41Z | |
| dc.description | We establish existence and uniqueness for the martingale problem associated with a system of degenerate SDE's representing a catalytic branching network. For example, in the hypercyclic case: $$dX_{t}^{(i)}=b_i(X_t)dt+\sqrt{2γ_{i}(X_{t}) X_{t}^{(i+1)}X_{t}^{(i)}}dB_{t}^{i}, X_t^{(i)}\ge 0, i=1,..., d,$$ where $X^{(d+1)}\equiv X^{(1)}$, existence and uniqueness is proved when $γ$ and $b$ are continuous on the positive orthant, $γ$ is strictly positive, and $b_i>0$ on $\{x_i=0\}$. The special case $d=2$, $b_i=θ_i-x_i$ is required in work of Dawson-Greven-den Hollander-Sun-Swart on mean fields limits of block averages for 2-type branching models on a hierarchical group. The proofs make use of some new methods, including Cotlar's lemma to establish asymptotic orthogonality of the derivatives of an associated semigroup at different times,and a refined integration by parts technique from Dawson-Perkins]. As a by-product of the proof we obtain the strong Feller property of the associated resolvent. | |
| dc.identifier | https://arxiv.org/abs/0801.3257 | |
| dc.identifier | http://arxiv.org/abs/0801.3257 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146349 | |
| dc.subject | Probability | |
| dc.subject | 60H10 | |
| dc.title | Degenerate stochastic differential equations arising from catalytic branching networks | |
| dc.type | text |