Some stochastic particle methods for nonlinear parabolic PDEs

Infinite dimensional backstepping for nonlinear parabolic PDEs

On the Unique Solvability of Some Nonlinear Stochastic Pdes

The Cauchy problem for 1-dimensional nonlinear stochastic partial differential equations is studied. The uniqueness and existence of solutions in Hp(T )-space are proved. 1991 Mathematics Subject Classification. 60H15, 35R60.

Strong invariance and noise-comparison principles for some parabolic stochastic PDEs∗

We consider a system of interacting diffusions on the integer lattice. By letting the mesh size go to zero and by using a suitable scaling, we show that the system converges (in a strong sense) to a solution of the stochastic heat equation on the real line. As a consequence, we obtain comparison inequalities for product moments of the stochastic heat equation with different nonlinearities.

BIRKHOFF NORMAL FORM FOR SOME NONLINEAR PDEs

A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs

We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in [10], and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-time approximation and derives a bound on the discretizat...