How to raise rent on your tenant

[Tone Church]

My tenant is not on a lease with me. He had one with the previous owner of the property but I never established one with him. It has been 8 months since I bought the house. He is paying about $350/month below market rates ($1,200 vs $1,550 / month). What considerations or legal implications should I be thinking about before telling him his rent will be going up?

Also, am I required by New York state law to hold tenants deposit in escrow?