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Joan Rivers, Melissa Rivers

Christopher Polk/Getty Images

Joan Rivers is a fighter.

As the E! Fashion Police host remains hospitalized at Mount Sinai Hospital in New York City, a source reveals the comedian is making small, but positive, steps.  

"It's a slow process, but she's on the road to recovery," a source close to the situation tells E! News exclusively. "She's getting better. Don't believe all this ridiculous speculation."

Joan stopped breathing while undergoing a minor throat procedure Aug. 28 in New York City. She was then rushed to the hospital where she was placed in a medically induced coma.

Her daughter, Melissa Rivers, flew across the country the same day with her son, Cooper, to be by the comic legend's side.

"She is a rock. She is calmer than I've ever seen her," the source told E! News in regards to Melissa. "All these reports about doomsday are not true. She is her mother's daughter and she's tough as nails. She's the person keeping everyone together."

The insider added, "She's focused on one thing: Her mother's health."

Joan remains in stable, yet critical, condition. On Sunday, Melissa thanked fans for all their prayers and well wishes.

"Thank you for your continued love and support," she said in a statement. "We are keeping our fingers crossed."

Our thoughts and prayers continue to go out to the Rivers family at this time.