is devoted to the proof of the existence and uniqueness of SDEs with jumps under global Lipschitz condition. In chapter 3, we focus on the strong convergence of the CSTM and the stability analysis of both CSTM and STM. In chapter 4, under non-global Lipschitz condition we investigate the strong convergence of the compensated tamed Euler scheme. In chapter 5, under non-global Lipschitz condition, we investigate the strong convergence and stability of both semi-tamed Euler scheme and tamed Euler scheme. Our theoretical results are illustrated by numerical examples at the end of chapter 3, chapter 4 and chapter 5. \[chp: chap1 Basic Notions in probability theory and stochastic process\]

Basic notions in probability theory and stochastic process
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 Basic notions in probability theory 
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In this chapter, we present some basic concepts and results in probability theory and stochastic process useful to understand the notion of stochastic differential equations.

More details for this chapter can be found in [@Oksa], [@Oks] and [@Phi].

### **Basic notions in probability theory**

**\[$\sigma$- algebra\]**

Let $\Omega$ be a non-empty set.

1.  A $\sigma$-algebra (or $\sigma$-field) $\mathcal{F}$ on $\Omega$ is a family of subsets of $\Omega$ satisfying

    1.  $\Omega \in \mathcal{F}$.

    2.  $\forall A\in \mathcal{F}$, 