Markov Processes, Volume 1Academic Press, 1965 - Markov processes |
Contents
Preface Preface to the English edition Introduction 1 Modern definition of a Markov process | 1 |
Shift operators Infinitesimal and characteristic operators | 2 |
Diffusion processes Probabilistic solution of differential equations | 4 |
Copyright | |
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Common terms and phrases
a₁ additive functional Af(x arbitrary assume B-measurable function Banach space Borel sets bounded characteristic operator coincides compact Consequently continuous function converges coordinate system corollary corresponding defined by formula denote differentiable manifold diffusion process domain equation Euclidean space exit f₁ Feller process finite full measure function f GTMP Hence Hölder condition homogeneous implies inequality infinitesimal operator initial distribution interval Lebesgue measure linear operator M₂ Markov process minimum principle neighborhood o-algebra open set P₂ proof of theorem proved Remark right-continuous satisfies condition satisfies the condition semi-compact semigroup sequence set of full standard process stochastically continuous strong Markov process t₁ T₁f topology transition function P(t twice continuously differentiable W-functional weak infinitesimal operator Wiener process X-integrable µ dy