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Towards an Innovation Theory of Spatial Brownian Motion under Boundary Conditions
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E. Khmaladze
Veröffentlicht/Copyright:
25. Februar 2010
Abstract
Set-parametric Brownian motion b in a star-shaped set G is considered when the values of b on the boundary of G are given. Under the conditional distribution given these boundary values the process b becomes some set-parametrics Gaussian process and not Brownian motion. We define the transformation of this Gaussian process into another Brownian motion which can be considered as “martingale part” of the conditional Brownian motion b and the transformation itself can be considered as Doob–Meyer decomposition of b. Some other boundary conditions and, in particular, the case of conditional Brownian motion on the unit square given its values on the whole of its boundary are considered.
Key words and phrases:: Set-parametric Brownian motion; Doob–Meyer decomposition; set-parametric Brownian bridge; innovation process; Volterra operators
Received: 2001-03-06
Published Online: 2010-02-25
Published in Print: 2001-June
© Heldermann Verlag
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Artikel in diesem Heft
- Topological Spaces with the Strong Skorokhod Property
- Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes
- On a Characterisation of Inner Product Spaces
- On the Tail Estimation of the Norm of Rademacher Sums
- Entropy Numbers of Certain Summation Operators
- Proper Moving Average Representations and Outer Functions in Two Variables
- Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
- Towards an Innovation Theory of Spatial Brownian Motion under Boundary Conditions
- Entropy Numbers of Diagonal Operators of Logarithmic Type
- On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
- Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators
- Probability Measures with Big Kernels
- Hölder Versions of Banach Space Valued Random Fields
- Representations of Conditional Means
- On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
- On Stochastic Differential Equations in a Configuration Space
- On Accuracy of Improved χ2-Approximations
- Tractability of Tensor Product Linear Operators in Weighted Hilbert Spaces
Schlagwörter für diesen Artikel
Set-parametric Brownian motion;
Doob–Meyer decomposition;
set-parametric Brownian bridge;
innovation process;
Volterra operators
Artikel in diesem Heft
- Topological Spaces with the Strong Skorokhod Property
- Convergence to Zero and Boundedness of Operator-Normed Sums of Random Vectors with Application to Autoregression Processes
- On a Characterisation of Inner Product Spaces
- On the Tail Estimation of the Norm of Rademacher Sums
- Entropy Numbers of Certain Summation Operators
- Proper Moving Average Representations and Outer Functions in Two Variables
- Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
- Towards an Innovation Theory of Spatial Brownian Motion under Boundary Conditions
- Entropy Numbers of Diagonal Operators of Logarithmic Type
- On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
- Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators
- Probability Measures with Big Kernels
- Hölder Versions of Banach Space Valued Random Fields
- Representations of Conditional Means
- On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands
- On Stochastic Differential Equations in a Configuration Space
- On Accuracy of Improved χ2-Approximations
- Tractability of Tensor Product Linear Operators in Weighted Hilbert Spaces
