The proper way to interface a ESC to a Arduino is using the servo library commands, not analogWrite PWM commands. ESCs are built to emulate acting just like a servo from a control point of view. Also you will need to find out the proper 'arming' commands to activate the ESC from the arduino. Arming is a safety feature on ESC that's prevents them from starting off when first powering on. Usually it's a sequence of 100% signal for one second or so, 0% for one second or so, and wait for ESC to beep signifying it's ready to accept servo speed commands. Yours may have a different sequence so read the operators manual for the ESC.
Lefty