Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains

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Stochastic Portfolio Theory: an Overview (2009, unknown): “The theory developed by Bass & Perkins (2002) shows that the resulting system of stochastic differential equations, for i = 1, . . . , n, dXi(t) = 1 + α 2 ( X1(t) + . . . + Xn(t) ) dt + √ Xi(t) ( X1(t) + . . . + Xn(t) ) dWi(t), (12.2) determines the distribution of the ∆n+−valued diffusion process…”
Relative arbitrage in volatility-stabilized markets (2005, background): “It follows again from Bass & Perkins (2002) that the martingale problem, which has infinitesimal generator (Af)(x) = 1 2 (x1 + · · · + xn) ∑ni=1 ( xi D 2 iif(x) + (1 + α) Dif(x) ) , x ∈ (0,∞)n associated with (6.2), is well-posed; and straightforward computations give again constant variance and…”
The Black–Scholes equation in stochastic volatility models (2010, background): “Remark The pathwise uniqueness of solutions to (12) follows from [2] and Corollary IX.”
Degenerate Diffusion Operators Arising in Population Biology (2011, background): “Various extensions of these results, using a variety of functional analytic frameworks, were made by Athreya, Barlow, Bass Perkins, Sato, Cerrai and Clément, and others, see [1, 4, 5, 6, 7].”