FLC OF A CANADAIR REGIONAL JET; CL65; MADE A MISSED APCH DUE TO TCASII RA. APCH CTLR HAD GIVEN A TA; BUT SINCE THE RPTR WAS IMC AND TCASII RA ADVISED OF TFC CLBING WITHIN 300 FT OF THEIR ALT.

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I WAS THE PF AS WE TRACKED THE LOC INBOUND TO FYV ARPT AT 3000 FT MSL. WE HAD BEEN CLRED FOR THE LOC RWY 16 APCH TO FYV AND 3000 FT WAS THE APPROPRIATE ALT AT THIS POINT ON THE APCH. WE WERE ESTABLISHED ON THE LOC COURSE WHEN APCH CALLED TFC; PASSING R TO L 500 FT BELOW. THEY SAID THAT THEY WERE NOT IN CONTACT WITH THAT TFC. WE WERE IN IMC CONDITIONS; DID NOT ESTABLISH VISUAL CONTACT WITH THE TFC; BUT DID NOTICE IT ON OUR TCASII. SHORTLY AFTERWARDS WE GOT A TA 'TFC; TFC' TCASII WARNING AS THE TFC CLBED TO 400 FT BELOW US. ALMOST IMMEDIATELY; WE GOT AN RA 'MONITOR VERT SPD' TCASII WARNING AS THE TFC CONTINUED TO CLB TO 300 FT BELOW US AND AT 12 O'CLOCK POS. AT THIS TIME I DISCONNECTED THE AUTOPLT AND CLBED TO 4000 FT. ATC WAS INFORMED THAT WE WERE MISSING THE APCH AND TOLD US TO MAINTAIN 3000 FT AND TURN R TO 270 DEGS. WE WERE THEN VECTORED FOR ANOTHER UNEVENTFUL APCH. ATC SAID THAT THEY WERE GOING TO TRACK THE OTHER ACFT. I WAS A LITTLE CONCERNED ABOUT VACATING 3000 FT FOR 4000 FT WITHOUT A CLRNC TO DO SO; BUT FELT THAT THE DANGER FROM THE CLBING INTRUDER ACFT WAS A MUCH BIGGER THREAT.