István Gyöngy
University of Edinburgh
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Featured researches published by István Gyöngy.
Potential Analysis | 1998
István Gyöngy
We approximate quasi-linear parabolic SPDEs substituting the derivatives in the space variable with finite differences. When the nonlinear terms in the equation are Lipschitz continuous we estimate the rate of Lp convergence of the approximations and we also prove their almost sure uniform convergence to the solution. When the nonlinear terms are not Lipschitz continuous we obtain this convergence in probability, if the pathwise uniqueness for the equation holds.
Potential Analysis | 1998
István Gyöngy
We prove that Eulers approximations for stochastic differential equations on domains of ℝd converge almost surely if the drift satisfies the monotonicity condition and the diffusion coefficient is Lipschitz continuous.
Stochastic Processes and their Applications | 1998
István Gyöngy
We prove existence, uniqueness and comparison theorems for a class of semilinear stochastic partial differential equations driven by space-time white noise. The class of equations we investigate contains as special cases the stochastic Burgers equation and the reaction-diffusion equations perturbed by space-time white noise.
Potential Analysis | 2005
István Gyöngy; Annie Millet
Abstract Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.
Stochastic Processes and their Applications | 2000
István Gyöngy; Carles Rovira
We prove existence, uniqueness and comparison theorems for a class of parabolic semilinear stochastic partial differential equations with nonlinearities of polynomial growth in the case of several space dimension.
Potential Analysis | 2009
István Gyöngy; Annie Millet
Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rates of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type.
Czechoslovak Mathematical Journal | 2001
István Gyöngy; Teresa Martinez
We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.
IEEE Transactions on Electron Devices | 2016
Neale Dutton; István Gyöngy; Luca Parmesan; Salvatore Gnecchi; Neil Calder; Bruce R. Rae; Sara Pellegrini; Lindsay A. Grant; Robert Henderson
A CMOS single-photon avalanche diode (SPAD)-based quarter video graphics array image sensor with 8-μm pixel pitch and 26.8% fill factor (FF) is presented. The combination of analog pixel electronics and scalable shared-well SPAD devices facilitates high-resolution, high-FF SPAD imaging arrays exhibiting photon shot-noise-limited statistics. The SPAD has 47 counts/s dark count rate at 1.5 V excess bias (EB), 39.5% photon detection probability (PDP) at 480 nm, and a minimum of 1.1 ns dead time at 1 V EB. Analog single-photon counting imaging is demonstrated with maximum 14.2-mV/SPAD event sensitivity and 0.06e- minimum equivalent read noise. Binary quanta image sensor (QIS) 16-kframes/s real-time oversampling is shown, verifying single-photon QIS theory with 4.6× overexposure latitude and 0.168e- read noise.
Siam Journal on Mathematical Analysis | 2005
István Gyöngy; Nicolai V. Krylov
We approximate the solution u of the Cauchy problem \begin{gather*} \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, \end{gather*} by splitting the equation into the system
Siam Journal on Mathematical Analysis | 2010
István Gyöngy; Nicolai V. Krylov