70 citations · 274 across the 23 of their papers we have counts for
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Harnack inequality for parabolic equations in double-divergence form with singular lower order coefficients
Istvan Gyöngy, Seick Kim
This paper investigates the Harnack inequality for nonnegative solutions to second-order parabolic equations in double divergence form. We impose conditions where the principal coe…
On -Solvability of Stochastic Integro-Differential Equations
István Gyöngy, Sizhou Wu
A class of (possibly) degenerate stochastic integro-differential equations of parabolic type is considered, which includes the Zakai equation in nonlinear filtering for jump diffus…
On solvability of integro-differential equations
Marta De León-Contreras, István Gyöngy, Sizhou Wu
A class of (possibly) degenerate integro-differential equations of parabolic type is considered, which includes the Kolmogorov equations for jump diffusions. Existence and uniquene…
On the solvability of degenerate stochastic partial differential equations in Sobolev spaces
Máté Gerencsér, István Gyöngy, Nicolai Krylov
Systems of parabolic, possibly degenerate parabolic SPDEs are considered. Existence and uniqueness are established in Sobolev spaces. Similar results are obtained for a class of eq…
Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space
I. Gyongy, N. Krylov
We give sufficient conditions under which the convergence of finite difference approximations in the space variable of possibly degenerate second order parabolic and elliptic equat…
An accelerated splitting-up method for parabolic equations
István Gyöngy, Nicolai Krylov
We approximate the solution of the Cauchy problem $$ \frac{\partial}{\partial t} u(t,x)=Lu(t,x)+f(t,x), \quad (t,x)\in(0,T]\times\bR^d, $$ $$ u(0,x)=u_0(x),\quad x\in\bR^d $$ b…