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Integral Transformations and Anticipative Calculus for Fractional Brownian Motions.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2005Copyright date: ©2005Edition: 1st edDescription: 1 online resource (144 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470404260
Subject(s): Genre/Form: Additional physical formats: Print version:: Integral Transformations and Anticipative Calculus for Fractional Brownian MotionsDDC classification:
  • 510 s;519.2/2
LOC classification:
  • QA274.22 -- .H8 2005eb
Online resources:
Contents:
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.
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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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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