István Gyöngy

Lattice Approximations for Stochastic Quasi-Linear Parabolic Partial Differential Equations driven by Space-Time White Noise II

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.

A note on Euler's Approximations

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.

Existence and uniqueness results for semilinear stochastic partial differential equations

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.

On Discretization Schemes for Stochastic Evolution Equations

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.

On Lp-solutions of semilinear stochastic partial differential equations

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.

Rate of Convergence of Space Time Approximations for Stochastic Evolution Equations

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.

On Stochastic Differential Equations with Locally Unbounded Drift

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.

A SPAD-Based QVGA Image Sensor for Single-Photon Counting and Quanta Imaging

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.

An Accelerated Splitting-up Method for Parabolic Equations

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