TY  - BOOK
AU  - Hu,Yaozhong
TI  - Integral Transformations and Anticipative Calculus for Fractional Brownian Motions
T2  - Memoirs of the American Mathematical Society
SN  - 9781470404260
AV  - QA274.22 -- .H8 2005eb 
U1  - 510 s;519.2/2 
PY  - 2005///
CY  - Providence
PB  - American Mathematical Society
KW  - Stochastic integrals
KW  - Gaussian processes
KW  - Fractional calculus
KW  - Integral transforms
KW  - Electronic books
N1  - Intro -- Contents -- Abstract -- Chapter 1. Introduction -- Chapter 2. Representations -- Chapter 3. Induced Transformation I -- Chapter 4. Approximation -- 4.1. Rate of Convergence When 0 &lt -- H &lt -- 1/2 -- 4.2. Rate of Convergence When 1/2 &lt -- H &lt -- 1 -- 4.3. Higher Order of Convergence When 3/4 &lt -- H &lt -- 1 -- 4.4. Best Approximation -- Chapter 5. Induced Transformation II -- 5.1. Operators Associated With Z[sub(H)](t,s) -- 5.2. Inverse Operator of T[sub(H,T)] -- 5.3. B[sub(H,T)]T[sub(H,T)] when 1/2 &lt -- H &lt -- 1 -- 5.4. T[sub(H,T)]B[sub(H,T)] for 1/2 &lt -- H &lt -- 1 -- 5.5. B[sub(H,T)]T[sub(H,T)] for 0 &lt -- H &lt -- 1/2 -- 5.6. T[sub(H,T)]B[sub(H,T)] for 0 &lt -- H &lt -- 1/2 -- 5.7. Transpose of  T[sub(H,T)] -- 5.8. The Expression for T[sub(H,T)]T*[sub(H,T)] -- 5.9. The transpose of  B[sub(H,T)] -- 5.10. The Expression of B*[sub(H,T)]B[sub(H,T)] -- 5.11. Extension of T*[sub(H,T)] and B*[sub(H,T)] -- 5.12. Representation of Brownian motion by fractional Brownian motion -- Chapter 6. Stochastic Calculus of Variation -- 6.1. Stochastic Integral for Deterministic Integrands -- 6.2. A Probability Structure Preserving Mapping -- 6.3. Stochastic Integral for General Integrands -- 6.4. Malliavin Derivatives -- 6.5. Note on Stochastic Integral for ffim -- Chapter 7. Stochastic Integration -- 7.1. Existence and Examples -- 7.2. Stochastic Integral ∫[sup(a)][sub(0)] f(t)dB[sup(H)][sub(t)] of different upper limits -- 7.3. An L[sub(p)]estimate -- 7.4. An Example -- Chapter 8. Nonlinear Translation (Absolute Continuity) -- Chapter 9. Conditional Expectation -- Chapter 10. Integration By Parts -- Chapter 11. Composition (ltô Formula) -- Chapter 12. Clark Type Representation -- Chapter 13. Continuation -- Chapter 14. Stochastic Control -- Chapter 15. Appendix -- Bibliography
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114136
ER  -