Titlebook: Stochastics in Finite and Infinite Dimensions; In Honor of Gopinath Takeyuki Hida,Rajeeva L. Karandikar,Jie Xiong Book 2001 Birkhäuser Bost

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Numerical Solutions for a Class of SPDEs with Application to Filtering,heme is based on the fact that the solutions of the SPDEs can be represented by the weighted empirical measure of an infinite system of interacting particles. There are two sources of error in the scheme, one due to finite sampling of the infinite collection of particles and the other due to the Eul

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On Equations of Stochastic Fluid Mechanics, for this setting is to understand the motion of fluid parcels in turbulent and randomly forced fluid flows. Stochastic Euler and Navier-Stokes equations for the undetermined components.(.) and σ(.)of the spatial velocity field are derived from first principles. The resulting equations include as pa

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Infinite Level Asymptotics of a Perturbative Chern-Simons Integral,3-manifolds, among them the linking number [3], [4]. Albeverio and his colleagues have been studying the integral for the abelian case by the Fresnel integral [1] and the non-commutative case (in the setting of Fröhlich-King [6]) by using a white noise distribution [2].

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Risk-Sensitive Dynamic Asset Management with Partial Information,onential Quadratic Gaussian) control problems have been studied as the analogue of LQG control, where the optimal controls are explicitly represented by using the solutions of matrix Riccati differential equations. In fact, in the case of the discrete time LEQG control problem, the representation of

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On the Zakai Equation of Filtering with Gaussian Noise, Recently, a similar filtering problem with fBm noise was considered in [.]. However, the authors considered a non—Markovian signal process. The assumption of the Markov property on the signal is realistic. This also leads to a recursive equation, which is easily tractable, and is widely studied ([., .]).

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Risk-Sensitive Dynamic Asset Management with Partial Information,by using the solutions of matrix Riccati differential equations. In fact, in the case of the discrete time LEQG control problem, the representation of the optimal strategy was obtained by Whittle [.] and in the continuous time case by Bensoussan and Van Schuppen [.].

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Existence of a Strong Solution for an Integro-Differential Equation and Superposition of Diffusion nctions with α-Hölder continuous .-th derivatives and with all .-th derivatives for . ≤ . vanishing at infinity, and.. This ensures the existence of a Feller process associated with the generator . + . in the usual way.

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