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Degenerate stochastic differential equations arising from catalytic branching networks

   
@article{EJP568,
	author = {Richard Bass and Edwin Perkins},
	title = {Degenerate stochastic differential equations arising from catalytic branching networks},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {13},
	year = {2008},
	keywords = {stochastic differential equations; perturbations; resolvents; Cotlar's lemma; catalytic branching; martingale problem; degenerate diffusions},
	abstract = {We establish existence and uniqueness for the martingale problem associated with a system of degenerate SDE's representing a catalytic branching network.  The drift and branching coefficients are only assumed to be continuous and satisfy some natural non-degeneracy conditions.  We assume at most one catalyst per site as is the case for the hypercyclic equation.  Here the two-dimensional case with affine drift is required in work of [DGHSS] 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 [DP1].},
	pages = {no. 60, 1808-1885},
	issn = {1083-6489},
	doi = {10.1214/EJP.v13-568},    
        url = {http://ejp.ejpecp.org/article/view/568}}