A bit of googling found some conflicting ones...
Asset inflation occurs when the prices of financial assets are rising even though they are already above their intrinsic or underlying value. Hence, to establish asset inflation, the intrinsic value of equities and houses must be first determined.
The latter problem is obviously rather hard.
Another, more terse definition seem to roughly in the same vein:
asset prices to levels not supported by economic fundamentals (“asset price inflation”).
So this more or less the same thing as a "bubble", I think (and also as vague).
there have been several episodes around the world in which property prices or the value of sharemarket equities have risen significantly, even while consumer prices and workers' wages remained relatively stable. Such asset price inflations [...]
This seems an easier thing to measure in practice, but it's clearly not positing a deviation from an absolute/intrinsic value, at least in this snippet.
Overall asset price inflation equals the (implicitly weighted) sum of the fundamental component of asset price inflation and the bubble component of asset price inflation. [...] The fundamental component of asset price inflation is assumed to be a function of lagged inflation, output growth, and an error term that captures unexpected changes in the fundamental component of asset price inflation. [...] The asset price bubble component is modeled as being exogenous. This specification is somewhat arbitrary because economists do not have good empirical models of asset price bubbles.
But clearly in this view asset inflation is not the same as just a bubble...
not only Japan but also many countries [...] experienced big changes in asset prices, or so-called "asset price inflation" and "asset price deflation"
Probably the most trivial definition, i.e. (nominal or real?) increase in asset prices. Later in the paper he graphs for instance "real aggregate asset price indices" but also "nominal residential housing prices", so I'm not sure if his definition of asset inflation is in real or nominal terms.
So does any of these definitions have significant adoption in the literature? Are there more meanings for the term? Does any other definition of the term have substantial following?