Fully nonlinear stochastic PDE with semilinear stochastic dependence
By Pierre-Louis Lions, Panagiotis E. Souganidis. 2000
74 citations recorded by the source corpus.
Abstract We study in this Note scalar fully nonlinear stochastic second order partial differential equations, possibly, degenerate with a semilinear stochastic dependence. We introduce a notion of stochastic viscosity solutions adapted to that class of equations. And we show general existence, uniqueness and regularity results.
Subfields: Applied Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/a5fa15f7aa62591c906bc1af88588e5a4d6c3791
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In Applied Mathematics
- Panagiotis E. Souganidis
- Benoit Perthame
- Peter K. Friz
- Pierre-Louis Lions
- M. Caruana
- S. Armstrong
- Nader Masmoudi
- Russell W. Schwab
In Finance
- Peter K. Friz
- Panagiotis E. Souganidis
- Harald Oberhauser
- M. Caruana
- Benoit Perthame
- Pierre-Louis Lions
- Nicolas Victoir
- Benjamin Gess
Citations in the corpus
- Scalar conservation laws with rough (stochastic) fluxes (2013, methodology): “Following the earlier considerations as well as analogous problem for Hamilton-Jacobi equations ([20] we assume that, for each v ∈ R and T > 0, the initial value problem dΨ = Φ(Ψ) ◦ dW̃ in (0,∞), Ψ(0) = v, (42)”
- A (rough) pathwise approach to a class of non-linear stochastic partial differential equations (2009, background): “the matter is far from straight-forward: a transformation based on the (stochastic/rough) flow associsted to G, see [37], leads to a transformed PDE which does not fit in the standard viscosity theory and we shall return to this in future work.”