In this paper, we apply first and higher-order Euler discretizations to compare dynamic systems in discrete and continuous time. In addition, we stress the difference between backward and forward-looking approximations. Focussing on local bifurcations, we find that time representation is neutral and asymptotically neutral for models with saddle-node and Hopf bifurcations, respectively. Converse...

A discretization of an optimal control problem a stochastic parabolic equation driven by multiplicative noise is analyzed. The state discretized the continuous piecewise linear element method in space and backward Euler scheme time. convergence rate $$ O(\tau ^{1/2} + h^2) rigorously derived.

We consider the problem of designing robust numerical integration scheme solution a one-dimensional SDE with non-globally Lipschitz drift and diffusion coefficients behaving as $x^{\alpha }$, $\alpha >1$. propose an (semi-explicit) exponential-Euler for which we obtain theoretical convergence rate weak error. To this aim, analyze $C^{1,4}$ regularity associated backward Kolmogorov PDE using its...

background: in this paper we compare a highly accurate supervised to an unsupervised technique that uses breast thermal images with the aim of assisting physicians in early detection of breast cancer. methods: first, we segmented the images and determined the region of interest. then, 23 features that included statistical, morphological, frequency domain, histogram and gray-level co-occurrence ...

We consider the simulation of a system decoupled forward–backward stochastic differential equations (FBSDEs) driven by pure jump Lévy process L and an independent Brownian motion B . allow to have infinite activity. Therefore, it is necessary for employ finite approximation its measure. use generalized shot noise series representation method [26] approximate driving compute p error, ≥ 2, betwee...