Schramm–Loewner evolution ( $$\hbox {SLE}_\kappa $$ ) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by $$\sqrt{\kappa }$$ times Brownian motion. This yields a (half-plane) valued random field $$\gamma = \gamma (t, \kappa ; \omega )$$ . (Hölder) regularity of in $$\gamma (\cdot ,\kappa ;\omega $$ ), a.k.a. SLE trace, has been...
We consider deterministic fast–slow dynamical systems on $$\mathbb {R}^m\times Y$$ of the form $$\begin{aligned} {\left\{ \begin{array}{ll} x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} a\big (x_k^{(n)}\big ) + n^{-1/\alpha } b\big (x_k^{(n)}\big ) v(y_k), \\ y_{k+1} = f(y_k), \end{array}\right. } \end{aligned}$$ where $$\alpha \in (1,2)$$ . Under certain assumptions we prove convergence of...
We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend the class of equations studied so far by the last two authors.
We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend the class of equations studied so far by the last two authors.
We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend the class of equations studied so far by the last two authors.
