# On the Existence of Semimartingales with Continuous Characteristics

## TL;DR

This paper proves the existence of a class of semimartingales with continuous local characteristics under certain growth conditions, using approximation, tightness, and martingale problem techniques.

## Contribution

It establishes the existence of semimartingales with continuous characteristics satisfying Lyapunov or linear growth conditions, including path-dependent cases.

## Key findings

- Existence of quasi-left continuous semimartingales with continuous local characteristics.
- Application of approximation and tightness methods in the proof.
- Use of martingale problem approach for existence results.

## Abstract

We prove the existence of quasi-left continuous semimartingales with continuous local semimartingale characteristics which satisfy a Lyapunov-type or a linear growth condition, where latter takes the whole history of the paths into consideration. The proof is based on an approximation and a tightness argument and the martingale problem method.