You question is extremely broad. You're asking about the class of all SDEs. I'm assuming that you're interested in numerically integrating some form of SDE in order to estimate parameters.

A comprehensive introduction to the subject of SDE integration is Kloeden & Platen's book Numerical Solution of Stochastic Differential Equations, which, style- and code-wise is a bit dated now, but is still good. For the Matlab user, another fine (and shorter) introduction is this paper:

Desmond J. Higham, 2001, An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations, SIAM Rev. (Educ. Sect.), 43 525–46. http://dx.doi.org/10.1137/S0036144500378302

The demonstration Matlab files listed in the paper can be found here now.

Best method? Like with ODEs, *there is no best method*. It depends on the system. Adaptive step-size Runge-Kutta methods work for a huge class of ODE problems, but SDEs, with their noise/diffusion term, are more complicated. Without knowing anything about your system (the diffusion function $\sigma(x_t,\theta,t)$ in particular) or what stochastic formulation you're using, I can't say much. To start, use the Euler-Maruyama method if you have an Itô SDE or additive noise (i.e., the diffusion does not depend on the state variable, $\sigma(x_t,\theta,t) = \sigma(\theta,t)$) and the Euler-Heun method if you have a Stratonovich-formulated SDE with non-additive noise. These are the workhorses. Higher-order schemes are trickier to implement and are usually designed for particular types of systems/noise.

Finally, if you want a Matlab Toolbox that is still under active development, is much faster, and will be easy to use if you've ever used Matlab's ODE suite (e.g., `ode45`

), try my SDETools Matlab Toolbox for the Numerical Solution of Stochastic Differential Equations hosted on GitHub.