Transition probabilities for degenerate diffusions arising in population genetics

DOI10.1007/s00440-018-0840-2zbMath1417.35040arXiv1608.02119OpenAlexW2495514969MaRDI QIDQ1729702

Camelia A. Pop, Charles L. Epstein

Publication date: 28 February 2019

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.02119

zbMATH Keywords

fundamental solutionMarkov processestransition probabilitiescaloric measuredegenerate elliptic operatorsDirichlet heat kernelhitting distributionscompact manifold with corners

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Diffusion processes (60J60)

Related Items (9)

Harmonic analysis on graphs via Bratteli diagrams and path-space measures ⋮ \(C^0\)-estimates and smoothness of solutions to the parabolic equation defined by Kimura operators ⋮ Differentiability of semigroups of stochastic differential equations with H\"older-continuous diffusion coefficients ⋮ The fundamental solution to 1D degenerate diffusion equation with one-sided boundary ⋮ Existence, uniqueness and the strong Markov property of solutions to Kimura diffusions with singular drift ⋮ Boundary estimates for a degenerate parabolic equation with partial Dirichlet boundary conditions ⋮ Initial-boundary value problems for conservative Kimura-type equations: solvability, asymptotic and conservation law ⋮ Fundamental solution to 1D degenerate diffusion equation with locally bounded coefficients ⋮ Parabolic and elliptic equations with singular or degenerate coefficients: The Dirichlet problem

Cites Work

• A hierarchical extension scheme for solutions of the Wright-Fisher model
• \(C^0\)-estimates and smoothness of solutions to the parabolic equation defined by Kimura operators
• A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations
• Well-posedness of the martingale problem for some degenerate diffusion processes occurring in dynamics of populations
• Formulas for diffusion approximations of some gene frequency models
• Schauder estimates for a class of second order elliptic operators on a cube.
• The Feynman-Kac formula and Harnack inequality for degenerate diffusions
• Doubling properties for second order parabolic equations.
• Degenerate stochastic differential equations and super-Markov chains
• Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
• Boundary estimates for a degenerate parabolic equation with partial Dirichlet boundary conditions
• Schauder estimates for a degenerate second order elliptic operator on a cube
• Differentiable manifolds
• The uniqueness of hierarchically extended backward solutions of the Wright–Fisher model
• The Fundamental Solution to the Wright–Fisher Equation
• Harnack Inequalities and Heat Kernel Estimates for Degenerate Diffusion Operators Arising in Population Biology
• Degenerate Diffusion Operators Arising in Population Biology
• Existence, uniqueness and the strong Markov property of solutions to Kimura diffusions with singular drift
• On a class of degenerate elliptic operators arising from Fleming-Viot processes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Transition probabilities for degenerate diffusions arising in population genetics