Photo: Paul Bruinooge/getty

Asia Argento Anthony Bourdain

Asia Argentois paying tribute to the lateAnthony Bourdain.

On Friday, the 45-year-old actress marked what would’ve been Bourdain’s 65th birthday on social media.

Sharing aseries of photographs and videosof the chef on Instagram, Argento began the caption of her post, writing, “Celebrating the most incredible man I have ever met.”

“Missing you every day. Cherishing each moment we shared in our life together,” she continued. “I feel your presence and your strength.”

“You shine so bright within me,” added Argento. “I love you my A. Happy birthday ❤️.”

“It is with extraordinary sadness we can confirm the death of our friend and colleague, Anthony Bourdain,” the network said in a statement. “His love of great adventure, new friends, fine food and drink, and the remarkable stories of the world made him a unique storyteller. His talents never ceased to amaze us and we will miss him very much. Our thoughts and prayers are with his daughter and family at this incredibly difficult time.”

Never miss a story — sign up forPEOPLE’s free daily newsletterto stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.

In a statement provided to PEOPLE, the U.S. Embassy in Paris said, “We can confirm the death of Anthony Bourdain in the Haut-Rhin department of France. We extend our sincere condolences to friends and family. We stand ready to provide appropriate consular service. Out of respect for the family at this difficult time we have no further comment.”

RELATED VIDEO: The Restaurant Where Anthony Bourdain Began His Culinary Career Will Reopen for a Weekend

“People say I murdered him. They say I killed him,” she said through tears in the interview. “People need to think that he killed himself for something like this? He had cheated on me too. It wasn’t a problem for us. He was a man who traveled 265 days a year. When we saw each other we took really great pleasure in each other’s company. But we are not children. We are grown ups.”

“Anthony was 62, I was 42. We had lives, we had wives and husbands, we had children,” she continued. “I cannot think of Anthony as somebody who would do an extreme gesture like this for something like that.”

source: people.com