Conditions of detonation initiation induced by a supersonic sphere in a stoichiometric hydrogen/oxygen mixture with 70% argon dilution are investigated numerically and theoretically. Transitions of the two extremes, shock-induced combustion and detonation initiation, are examined over pressures ranging between 0.2 and 10 bar. Numerical results show a very distinct detonation initiation boundary that separates the detonatable and undetonatable regions. A good agreement is shown through the comparison of the numerical results with the recent experimenetal data. Additionally, a theoretical investigation on the determination of detonation initiation boundary is carried out by introducing a concept of the kinetic limit. The kinetic limit is defined by the ignition Damköhler number. A joint theory for the determination of the detonation initiation boundary is presented by relating the present kinetic limit defined by the unity ignition Damköhler number with the energy limit given by Lee. Comparison between the theory and the experiment over a wide pressure range shows that the detonation initiation boundary can be well defined by the present joint theory.