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Davie’s exact coupling technique for stochastic differential equations may be used to enhance the convergence of the multilevel Monte Carlo (MC) methodology. Giles developed the multilevel MC technique, which is based on executing the MC method several times with various time increments. It cuts computing costs significantly by executing most simulations at a low cost. The essential concept behind the multilevel MC approach with the exact coupling is discussed in this article. Numerical implementation reveals significant computational savings, which supports the analysis.

This study aimed to develop efficient numerical techniques with the same accuracy level as exact solutions of stochastic differential equations (SDEs). The MATLAB program was used to find solutions for the Euler and trivial coupling methods. The results of these methods were then compared and analyzed. The results show that Euler and trivial coupling methods give the same strong convergence. Furthermore, we demonstrated that these methods achieve strong convergence with a standard order of one-half to the exact solution of the SDE. Moreover, the Euler method is characterized by its speed, ease of application and ability to find solutions through computer programs. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the sufficient conditions for null controllability of noninstantaneous impulsive Hilfer fractional stochastic integrodifferential system with the Rosenblatt process and Poisson jump. The required results are obtained based on fractional calculus, stochastic analysis, and Sadovskii's fixed point theorem. Finally, an example is given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic Hantavirus infection model is constructed. The existence, uniqueness, and boundedness of the positive solution of the stochastic Hantavirus infection model are derived. The conditions for the extinction of the Hantavirus infection from the stochastic system are obtained. Furthermore, the criteria for the presence of a unique ergodic stationary distribution for the Hantavirus infection model are established using a suitable Lyapunov function. Finally, the importance of environmental noise in the Hantavirus infection model is illustrated using the Milstein method. [ABSTRACT FROM AUTHOR]

We compare Milstein and exact coupling methods for the strong approximation of solutions to stochastic differential equations (SDE), which are driven by Brownian motion. Both of these methods attain an order one convergence under the nondegeneracy assumption of the diffusion term for the exact coupling method. We also compare their implementation using MATLAB. A particular two-dimensional SDE is used in the implementation for comparing their results. Moreover, the performance of both methods and the amount of time required to obtain the result are also analyzed. It is interesting to mention that this comparison is very important in several areas, such as stochastic analysis, financial mathematics and some physical applications. [ABSTRACT FROM AUTHOR]