Jazz And Classical Improvisation

Hey folks, I wonder how classical music approaches improvisation. Is there anything such? especially in chamber format like jazz combo? Also, I want to ask little bit about the theory. Say if I have this progression in Cmajor (Dm - Db - C), and if I do some impro at the passing chord Db with the arpeggio (db f ab), then I resolved the ab to g when the Cmajor chord hit, that would make db unresolved. Is it right in classical music perspective? 

Thanks.

There is improvisation in modern day classical music, but it's often very experimental/niche stuff. Some more well known composers use it, i.e. in Marc Anthony Turnage's "Blood on the Floor", where Jazz musicians improvise alongside classical musicians reading normal notation. It can also be used in contemporary avant-garde pieces in brief spurts, but it is usually very controlled, i.e. giving a fixed rhythm but allowing freedom of pitches or vice versa.

Most graphic scores require a degree of improvisation to realise, and a number of modern composers also improvise on various instruments. "Classical" improvisation tends to be performed in sets at various venues supporting that kind of thing (e.g. london's cafe oto, new york's roulette, etc) and is often affiliated with various minimal/post-minimal and/or Lachenmann-ish movements.

if not contemporary experimental stuff tonal improvisation is still kept somewhat alive in the modern french organ tradition by the likes of olivier latry and daniel roth. richard grayson has made a thing out of it. there are probably some performers left like rzewski who still improvise cadenzas in old scores.

Great, I'll check them out. I've heard some of them like Kenny Barron's Classical Jazz quartet who plays classical piece in jazz idiom, or Jazz guitarist Ted Greene who improvises jazz standard tunes in baroque style. But never heard of classical players.

Richard Grayson is considered by many to be the best non-jazz improviser alive. You can check many videos of improvised performances here http://www.youtube.com/user/improvelectronic.

He accepts any requests from the audience to take either an original theme or a piece by a composer and play it in a period style or int the manner of another composer; for example "Rite of Spring" in the style of Mozart > 

In the past they had the basso continuo part that was improvised over a figured bass and sometimes musicians would improvise their cadenza although I believe it was more often written out in advance.