Transition operators of diffusions reduce zero-crossing

DOI10.1090/S0002-9947-99-02341-7zbMath0929.60058arXivmath/9801146OpenAlexW1497629003MaRDI QIDQ4226677

Ruth J. Williams, Steven N. Evans

Publication date: 27 January 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9801146

zbMATH Keywords

diffusionpartial differential equationmeasure valued processesmartingale problemsign changesvariation diminishingzero crossing

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Diffusion processes (60J60) Transition functions, generators and resolvents (60J35) Second-order parabolic equations (35K10)

Cites Work

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• Classes of solutions of linear systems of partial differential equations of parabolic type
• Coincidence probabilities
• Classical diffusion processes and total positivity
• On the total - and strict total - positivity of the kernels associated with parabolic initial boundary value problems
• Stopping times and tightness
• Total Positivity of Fundamental Solutions of Parabolic Equations
• The zero set of a solution of a parabolic equation.
• Variation Diminishing Transformations: A Direct Approach to Total Positivity and its Statistical Applications
• Diffusions and Elliptic Operators
• Total Positivity, Absorption Probabilities and Applications