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  "body": "\n## Summary\n\nA semimartingale is a process that is the sum of a [[local martingale|XC2YPC2BSW]] and a process of finite variation.\nSemimartingales are the largest natural class of integrators for stochastic integrals.\nBrownian motion, Lévy processes and solutions of stochastic differential equations are semimartingales.\n\n## Explanations\n\n### L1 human\n\nA semimartingale is \"noise plus drift\".\nThe noise part is a fair game, like Brownian motion, and the drift part changes in a tame way, like an ordinary function of bounded variation.\nFor example, a share price modelled as $X_t = W_t + 0.05\\, t$ is a fair-game noise $W_t$ plus a steady drift.\nItô's formula and stochastic integration work for exactly this kind of process.\n",
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