We study systems of stochastic differential equations describing positions x1, x2, . . . , xp of p ordered particles, with inter-particles repulsions of the formWe show the existence of strong and pathwise unique non-colliding solutions of the system with a colliding initial point x1(0) ≤ . . . ≤ xp(0) in the whole generality, under natural assumptions on the coefficients of the equations.2010 Mathematics Subject Classification. 60J60, 60H15.
Abstract. Multidimensional and matrix versions of the Yamada-Watanabe theorem are proved. They are applied to particle systems of squared Bessel processes and to matrix analogues of squared Bessel processes: Wishart and Jacobi matrix processes.
We show that any R d \{0}-valued self-similar Markov process X, with index α > 0 can be represented as a path transformation of some Markov additive process (MAP) (θ, ξ) in S d−1 × R. This result extends the well known Lamperti transformation. Let us denote by X the self-similar Markov process which is obtained from the MAP (θ, −ξ) through this extended Lamperti transformation. Then we prove that X is in weak duality with X, with respect to the measure π(x/ x ) x α−d dx, if and only if (θ, ξ) is reversible with respect to the measure π(ds)dx, where π(ds) is some σ-finite measure on S d−1 and dx is the Lebesgue measure on R. Besides, the dual process X has the same law as the inversionThese results allow us to obtain excessive functions for some classes of self-similar Markov processes such as stable Lévy processes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.