From an economics standpoint, the fall in output has caught up with the fall in demand, which should prevent further deterioration in industrial production. Indeed, whilst retrospective indicators show no sign of improvement, current sentiment & demand indicators such as US & UK Manufacturing PMIs show signs of improvement, as the chart below demonstrates.

Indeed, Fed Chairman, Ben Bernanke, commented this week that:
"Recently we have seen tentative signs that the sharp decline in economic activity may be slowing, for example, in data on home sales, home building and consumer spending, including sales of new motor vehicles... A levelling out of economic activity is the first step toward recovery... [However,] we will not have a sustainable recovery without a stabilisation of our financial system and credit markets"
However, this is not cause for celebration as it is unlikely there will be a substantial bull market or significant economic recovery, merely a period of low growth punctuated with large fluctuations in asset prices, both up and down, for the foreseeable future. Indeed, this was the case in Japan, where, despite having peaked in December 1989 and falling 75% to March 2009, the TOPIX had a number of very large bear market rallies over the period (see chart below).
In fact, Barclays Capital noted this week that:
"US data have surprised to the upside to some extent over the past month or so. But sooner or later, the recovery in risky asset prices is unlikely to be sustained if some of the more important economies do not show convincing signs of recovery."
So, failing a sustained improvement above expectations, the current 25%+ rally in world equities may yet turn out to be another in a series of bear market rallies to come.

Therefore, expect interest rates to be kept low for the foreseeable future and inflation to remain subdued whilst growth remains stagnant. Moreover, given the amount of monetary stimulus that will eventually have to be removed, there is a high margin for policy error, increasing inflationary risks on a longer term perspective.