Regularity and Qualitative Properties of Solutions of Parabolic Equations for Measures

Regularity and Qualitative Properties of Solutions of Parabolic Equations for Measures

We obtain local and global estimates of solutions of parabolic equations for measures, assuming the integrability of the drift coefficient with respect to the solution and for arbitrary initial conditions. We describe the behavior of densities at infinity in terms of Lyapunov functions. The behavior...

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Veröffentlicht in:Theory of probability and its applications 2012-01, Vol.56 (2), p.252-279
1. Verfasser: Shaposhnikov, S. V.
Format: Artikel
Sprache:eng
Schlagworte:
Cauchy problems
Estimates
Investigations
Probability
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Beschreibung
Zusammenfassung:We obtain local and global estimates of solutions of parabolic equations for measures, assuming the integrability of the drift coefficient with respect to the solution and for arbitrary initial conditions. We describe the behavior of densities at infinity in terms of Lyapunov functions. The behavior of densities near the initial condition is investigated.
ISSN:0040-585X
1095-7219
DOI:10.1137/S0040585X9798539X