| Preface |
| Vector Integration / Chapter 1： |
| Preliminaries / 1.： |
| Banach spaces / A.： |
| Classes of sets / B.： |
| Measurable functions / C.： |
| Simple measurability of operator-valued functions / D.： |
| Weak measurability / E.： |
| Integral of step functions / F.： |
| Totally measurable functions and the immediate integral / G.： |
| The Riesz representation theorem / H.： |
| The classical integral / I.： |
| The Bochner integral / J.： |
| Convergence theorems / K.： |
| Measures with finite variation / 2.： |
| The variation of vector measures |
| Boundedness of [sigma]-additive measures |
| Variation of real-valued measures |
| Integration with respect to vector measures with finite variation |
| The indefinite integral |
| Integration with respect to gm |
| The Radon-Nikodym theorem |
| Conditional expectations |
| [sigma]-additive measures / 3.： |
| [sigma]-additive measures on [sigma]-rings |
| Uniform [sigma]-additivity |
| Uniform absolute continuity and uniform [sigma]-additivity |
| Weak [sigma]-additivity |
| Uniform [sigma]-additivity of indefinite integrals |
| Weakly compact sets in L[superscript 1 subscript F] ([mu]) |
| Measures with finite semivariation / 4.： |
| The semivariation |
| Semivariation and norming spaces |
| The semivariation of [sigma]-additive measures |
| The family m[subscript F,Z] of measures |
| Integration with respect to a measure with finite semivariation / 5.： |
| Measurability with respect to a vector measure |
| The seminorm m[subscript F,G](f) |
| The space of integrable functions |
| The integral |
| Properties of the space F[subscript D] (B, m[subscript F,G]) |
| Relationship between the spaces F[subscript D](m) |
| The indefinite integral of measures with finite semivariation |
| Strong additivity / 6.： |
| Extension of measures / 7.： |
| Applications / 8.： |
| Integral representation of continuous linear operations on L[superscript p]-spaces |
| Random Gaussian measures |
| The Stochastic Integral / Chapter 2： |
| Summable processes / 9.： |
| Notations |
| The measure I[subscript X] |
| Computation of I[subscript X] for predictable rectangles |
| Computation of I[subscript X] for stochastic intervals |
| The stochastic integral / 10.： |
| The space F[subscript D] [characters not reproducible] |
| The integral [function of] HdI[subscript X] |
| A convergence theorem |
| The stochastic integral H - X |
| The stochastic integral and stopping times / 11.： |
| Stochastic integral of elementary processes |
| Stopping the stochastic integral |
| Summability of stopped processes |
| The jumps of the stochastic integral |
| The completeness of the space L[superscript 1 subscript F,G](X) / 12.： |
| The Uniform Convergence Theorem |
| The Vitali and the Lebesgue Convergence Theorems |
| The stochastic integral of [sigma]-elementary and of caglad processes as a pathwise Stieltjes integral |
| Summability of the stochastic integral / 13.： |
| Summability criterion / 14.： |
| Quasimartingales and the Doleans measure |
| The summability criterion |
| Local summability and local integrability / 15.： |
| Definitions |
| Basic properties |
| Additional properties |
| Martingales / Chapter 3： |
| Stochastic integral of martingales / 16.： |
| Square integrable martingales / 17.： |
| Extension of the measure I[subscript M] |
| Summability of square integrable martingales |
| Properties of the space F[subscript F,G](M) |
| Isometrical isomorphism of L[superscript 1 subscript F,G](M) and L[superscript 2 subscript F]([mu subscript [M]]) |
| Processes with Finite Variation / Chapter 4： |
| Functions with finite variation and their Stieltjes integral / 18.： |
| Functions with finite variation |
| The variation function |g| |
| The measure associated to a function |
| The Stieltjes integral |
| Processes with finite variation / 19.： |
| Definition and properties |
| Optional and predictable measures |
| The measure [mu subscript X] |
| Summability of processes with integrable variation |
| The stochastic integral as a Stieltjes integral |
| The pathwise stochastic integral |
| Semilocally summable processes |
| Processes with Finite Semivariation / Chapter 5： |
| Functions with finite semivariation and their Stieltjes integral / 20.： |
| Functions with finite semivariation |
| The Stieltjes integral with respect to a function with finite semivariation |
| Processes with finite semivariation / 21.： |
| The semivariation process |
| The measure [mu]x |
| Summability of processes with integrable semivariation |
| Dual projections / 22.： |
| Dual projection of measures |
| Dual projections of processes |
| Existence of dual projections |
| Processes with locally integrable variation or semivariation |
| Examples of processes with locally integrable variation or semivariation |
| Decomposition of local martingales |
| The Ito Formula / Chapter 6： |
| The Ito formula / 23.： |
| Preliminary results |
| The vector quadratic variation |
| The quadratic variation |
| The process of jumps |
| Ito's formula |
| Stochastic Integration in the Plane / Chapter 7： |
| Order relation in R[superscript 2] / 24.： |
| The increment [Delta subscript zz], g |
| Right continuity |
| The filtration |
| The predictable [Sigma]-algebra |
| Stopping times |
| Stochastic processes |
| Extension of processes from R[superscript 2 subscript +] [times] [Omega] to R[superscript 2] [times] [Omega] |
| The seminorm I[subscript X] and the space F[subscript F,G](X) / 25.： |
| Properties of the stochastic integral / 26.： |
| Extension of I[subscript X] to P([infinity]) |
| Existence of left limits of X in L[superscript p subscript E] |
| Some properties of the integral [function of] HdI[subscript X] |
| Two-Parameter Martingales / Chapter 8： |
| A decomposition theorem / 27.： |
| The measures [characters not reproducible] and [mu subscript [M]] |
| Summability of the square integrable martingales in Hilbert spaces |
| The space F[subscript F,G](I[subscript M]) |
| Isometric isomorphism of L[superscript 1 subscript F,G](M) and L[superscript 2 subscript F]([mu subscript [M]]) |
| Two-Parameter Processes with Finite Variation / Chapter 9： |
| Functions with finite variation in the plane / 29.： |
| Monotone functions |
| Partitions |
| Variation corresponding to a partition |
| Variation of a function on a rectangle |
| Limits of the variation |
| Functions vanishing outside a quadrant |
| Variation of real-valued functions |
| Lateral limits |
| Measures associated to functions |
| [sigma]-additivity of the measure m[subscript g] / L.： |
| Processes with integrable variation / M.： |
| Two-Parameter Processes with Finite Semivariation / Chapter 10： |
| Functions with finite semivariation in the plane / 31.： |
| The Stieltjes integral for functions with finite semivariation in R[superscript 2] |
| Processes with finite semivariation in the plane / 32.： |
| References |
| Preface |
| Vector Integration / Chapter 1： |
| Preliminaries / 1.： |
図書
