Step 1: Understanding the Concept:
The stability of halogen oxides is governed by a combination of kinetic and thermodynamic factors.
Step 2: Detailed Explanation:
1. **Iodine Oxides:** These are the most stable because of higher thermodynamic stability resulting from high lattice energy and high covalent character (due to the large size and high polarizability of Iodine).
2. **Chlorine Oxides:** These are relatively stable due to kinetic factors and the ability of Chlorine to form multiple bonds (\( d\pi-p\pi \) bonding) with Oxygen, which stabilizes the structure.
3. **Bromine Oxides:** Bromine lacks both the high lattice energy stability of Iodine and the effective multiple bonding capability of Chlorine. Consequently, bromine oxides are the least stable and often exist only at low temperatures.
Thus, the decreasing order of stability is: \( \text{I}>\text{Cl}>\text{Br} \).
Step 3: Final Answer:
The correct stability order is \( \text{I}>\text{Cl}>\text{Br} \).