Abstract This work addresses the convergence of a split-step Euler type scheme (SSM) for numerical simulation interacting particle Stochastic Differential Equation (SDE) systems and McKean–Vlasov stochastic differential equations (MV-SDEs) with full super-linear growth in spatial interaction component drift, nonconstant Lipschitz diffusion coefficient. Super-linearity is understood sense that f...

Reactor noise, caused both by the probabilistic nature of the fission chains and external reactivity noises, is one of the basic topics in nuclear science and engineering, both in theory and practice. Modeling reactor noise (and neutron flux fluctuation in general) is traditionally performed by two main approaches: the stochastic transport equation for the probability generating function and th...

Bayesian approaches to statistical inference and system identification became practical with the development of effective sampling methods like Markov Chain Monte Carlo (MCMC). However, because the size and complexity of inference problems has dramatically increased, improved MCMC methods are required. Dynamical systems based samplers are an effective extension of traditional MCMC methods. Thes...

The mean-reverting square root process is a stochastic differential equation (SDE) that has found considerable use as a model for volatility, interest rate, and other financial quantities. The equation has no general, explicit, solution, although its transition density can be characterized. For valuing path-dependent options under this model, it is typically quicker and simpler to simulate the ...

This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates ...

The conformational transition pathway of sugar puckering between the C20-endo and C30-endo conformations of deoxyadenosine (dA) is reported using the stochastic difference equation (SDE) algorithm, which approximates longtime pathways. The south pucker is favored over the north by 0.34 0.2 kcal/mol, and the free energy barrier is about 2.2 0.2 kcal/mol above the global minimum. The transition o...

We model and verify noise in analog/RF designs using an automated theorem prover. We model the designs using stochastic differential equations (SDE), due to the statistical nature of noise. We find a closed form solution for the SDEs based on stochastic calculus, and then verify properties using the MetiTarski theorem prover. Our approach is illustrated on an RL High-Pass Filter and a Sample-an...

We study a class of methods for the numerical solution of the system of stochastic differential equations (SDEs) that arises in the modeling of turbulent combustion, specifically in the Monte Carlo particle method for the solution of the model equations for the composition probability density function (PDF) and the filtered density function (FDF). This system consists of an SDE for particle pos...

We show that the stochastic differential equation sSDEd model for the merger of two identical two-dimensional vortices proposed by Agullo and Verga f“Exact two vortices solution of Navier– Stokes equation,” Phys. Rev. Lett. 78, 2361 s1997dg is a special case of a more general class of SDE models for N interacting vortex filaments. These toy models include vorticity diffusion via a white noise f...

We prove an existence and uniqueness result for backward stochastic differential equations whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in aMarkovian framework, that is coupled with a forward SDE, our result provides a probabilis...