On a class of degenerate parabolic equations of Kolmogorov type

By Marco Di Francesco, Andrea Pascucci. 2005

107 citations recorded by the source corpus.

We adapt the Levi's parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9406987d454521fb1410ce6e586e5897dc6e67d5

How researchers see this paper

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In Applied Mathematics

1. Francesca Anceschi
2. Sergio Polidoro
3. Andrea Pascucci
4. Paolo Foschi
5. C. Imbert
6. Luis Silvestre

In Mathematical Physics

1. Francesca Anceschi
2. Sergio Polidoro
3. Paolo Foschi
4. Andrea Pascucci
5. C. Imbert
6. Luis Silvestre

Citations in the corpus

• Path dependent volatility (2008, methodology): “5) provided in Di Francesco and Pascucci (2005). Recently the free boundary and optimal stopping problems for American options in the HR model were studied in Pascucci (2007) and Di Francesco et al. (2007). An extension to the framework of term-structure modeling was given by Chiarella and Kwon (200”
• A survey on the classical theory for Kolmogorov equation (2019, background): “The following result is due to Di Francesco and Pascucci in [29].”
• On conditional McKean Lagrangian stochastic models (2011, background): “In [5], Di Francesco and Pascucci consider ultraparabolic PDEs of the type −∂sψ + 1 2 ∑ i, j a(i, ∂viv jψ + (y, v) · B∇(y,v)ψ = 0, where a and B are 2d × 2d matrices, and B has constant entries.”