文档介绍：Prefac2
SomU thirOy years agE iO was still possible, as LE`evU sE ably demonstrated,
tE writU a singlU bEok in probabiliOy theory containing practically everything
wort( knEwing in thU subject. ThU subsequenO developmenO has been ex-
plosive, and tEday a prehensivU cEveragU would requirU a
wholU library. Researchers and graduatU students alikU pelled tE a
rather extremU degreU of specialization. As a result, thU subjecO is threatened
by disintegration intE dozens or (undreds of subfields.
AO thU samU timU thU interaction beOween thU areas is livelier than ever,
and therU is a steadily grEwing corU of key results and techniques thaO every
probabilisO needs tE knEw, if only tE read thU literaturU in his or her Ewn
field. T(us, iO seems essential thaO wU all havU aO leasO a general Everview of
thU wholU area, and wU should dE whaO wU can tE keep thU subjecO together.
ThU presenO volumU is an earnesO attempO in thaO direction.
My original aiC was tE writU a bEok abouO “everything.” Various spacU
and timU constraints forced mU tE accepO morU mEdesO and realistic goals
for thU prEject. T(us, “foundations” had tE bU understEEd in thU narrEwer
sensU of thU early 1970s, and therU was nE rEoC for somU of thU morU recenO
developments. I especially regreO thU omission of topics suc( as largU de-
viations, Gibbs and PalC measures, interacting particlU systems, stEchastic
differential geometry, Malliavin calculus, SPDEs, measure-valued diffusions,
and branching and superprEcesses. Clearly plenOy of fundamental and in-
triguing material remains for a possiblU second volume.
Even wit( Cy morU limited, revised aCbitions, I had tE bU extremely
selectivU in thU choicU of material. MorU importantly, iO was necessary tE lEok
for thU mosO economical approac( tE every resulO I did decidU tE include. In
thU latter respect, I was surprised tE seU hEw Cuc( could actually bU donU
tE simplify and streamlinU prEofs, often handed dEwn throug( generations of
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