keywords: discontinuous drift, strong convergence rate, jump-diffusion stochastic differential equations, jump-adapted scheme, higher-order scheme

keywords: phase transformations, dislocation density, laminar cooling, stochastic model, grain size, JMAK model, random recrystallization, heterogeneity of microstructure

keywords: standard information, optimal algorithm, singular problems, r-fold integrated Brownian motion, stochastic Ito integrals

keywords: delay differential equations, one-side Lipschitz condition, locally Hölder continuous right-hand side function, Euler scheme

keywords: complexity, piecewise regularity, unknown switching hypersurface, locating singularities, initial value problems, derivative free scheme

keywords: Wiener process, adaptive step-size control, jump–diffusion SDEs, Merton's model, homogeneous Poisson process, random discretization

keywords: complexity, stochastic differential equations with jumps, lower error bounds, randomized Euler algorithm, Poisson random measure, countably dimensional Wiener process

keywords: complexity, initial value problems, infinite dimensional Banach space, Schauder basis, Galerkin-type algorithms, finite dimensional approximation

keywords: non standard assumptions, noisy information, Euler scheme, ODEs, local conditions, one-sided Lipschitz condition, Holder continuity

keywords: stochastic differential equations, existence and uniqueness, discontinuous drift, multi-dimensional jump diffusion, finite activity jumps, strong solutions

keywords: existence and uniqueness, jump-diffusion stochastic differential equation, equation, discontinuous drift, strong convergence rate, Euler-Maruyama scheme

keywords: delay differential equations, existence and uniqueness, Randomized Euler scheme, Caratheodory type conditions

keywords: identification, dislocation density, stochastic model, grain size, histograms, Bhattacharyya distance

keywords: Ito integral, standard information, average case setting, integral information, worst case setting

keywords: Monte Carlo methods, optimal algorithm, non standard assumptions, one-point approximation, lower bounds, asymptotic error

keywords: Monte Carlo, adaption, variance reduction, asymptotic constants

keywords: stochastic differential equations, Wiener process, Randomized Euler scheme, constant delay, Carathéodory-type conditions

keywords: delay differential equation, metallic materials, Euler method, strict error analysis, Runge-Kutta method

keywords: initial value problems, noisy information, deterministic of random noise, optimal solution, minimal cost

keywords: stability, optimality, noisy information, nth minimal error, randomized Euler algorithms, implicit schemes, explicit schemes

keywords: adaption, optimal algorithms, lower bounds, initial value problems, singularity, worst case errors

keywords: optimality, piecewise regularity, unknown switching hypersurface, locating singularities, adaption, upper and lower bounds, initial value problems

keywords: Wiener process, noisy information, optimal approximation, minimal error, analytic noise model, GPUs

keywords: asymptotic setting, optimal algorithm, stochastic integrals, r-fold integrated Poisson process, non adaptive standard information, adaptive standard information