2014/06/03 by Camelia A. Pop, Pop, Camelia A.
Mathematics · Economics, Econometrics and Finance · #Stochastic processes and statistical mechanics #Stochastic processes and financial applications #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1406.0745
Motivated by applications to proving regularity of solutions to degenerate\nparabolic equations arising in population genetics, we study existence,\nuniqueness and the strong Markov property of weak solutions to a class of\ndegenerate stochastic differential equations. The stochastic differential\nequations considered in our article admit solutions supported in the set\n[0,\∞)n\×\ℝm, and they are degenerate in the sense that the\ndiffusion matrix is not strictly elliptic, as the smallest eigenvalue converges\nto zero proportional to the distance to the boundary of the domain, and the\ndrift coefficients are allowed to have power-type singularities in a\nneighborhood of the boundary of the domain. Under suitable regularity\nassumptions on the coefficients, we establish existence of weak solutions that\nsatisfy the strong Markov property, and uniqueness in law in the class of\nMarkov processes.\n