The France striker is determined to do things his own way after completing his move from Ligue 1 champions Montpellier for a fee of around £10 million.
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Giroud has failed to find the target in his three appearances in the Premier League so far and warned that he could need time to adapt to the English game.
He was confident, however, that given time he would prove a success as one of three major signings made by manager Arsene Wenger during the summer.
"Everywhere I've been, I've needed some time to adapt, but in the end it's worked out well," Giroud told Le 10 Sport.
"I'm a level headed person who needs something to aim for to move forward, but I haven't given myself the task of replacing Van Persie.
"I want to take my place, win over the Arsenal fans in my own way."