Existence, uniqueness and the strong Markov property of solutions to Kimura diffusions with singular drift
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- by Camelia A. Pop PDF
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Abstract:
Motivated by applications to proving regularity of solutions to degenerate parabolic equations arising in population genetics, we study existence, uniqueness, and the strong Markov property of weak solutions to a class of degenerate stochastic differential equations. The stochastic differential equations considered in our article admit solutions supported in the set $[0,\infty )^n\times \mathbb {R}^m$, and they are degenerate in the sense that the diffusion matrix is not strictly elliptic, as the smallest eigenvalue converges to zero at a rate proportional to the distance to the boundary of the domain, and the drift coefficients are allowed to have power-type singularities in a neighborhood of the boundary of the domain. Under suitable regularity assumptions on the coefficients, we establish existence of solutions that satisfy the strong Markov property, and uniqueness in law in the class of Markov processes.References
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Additional Information
- Camelia A. Pop
- Affiliation: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street SE, Minneapolis, Minnesota 55455
- MR Author ID: 1014759
- Email: capop@umn.edu
- Received by editor(s): July 20, 2014
- Received by editor(s) in revised form: August 17, 2015, and September 2, 2015
- Published electronically: March 1, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 5543-5579
- MSC (2010): Primary 60J60; Secondary 35J70
- DOI: https://doi.org/10.1090/tran/6853
- MathSciNet review: 3646770