Stochastics in Finite and Infinite Dimensions

by Kallianpur, G.; Hida, Takeyuki; Karandikar, Rajeeva L.; Kunita, Hiroshi; Watanabe, Shinzo

• ISBN13: 9780817641375
• ISBN10: 0817641378
• Format: Hardcover
• Copyright: 2000-10-01
• Publisher: Birkhauser

Summary

During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong

Table of Contents

Preface	ix
A Glimpse into the Life and Work of Gopinath Kallianpur	xi
B. V. Rao
Publications of Gopinath Kallianpur	xxv
Precise Gaussian Lower Bounds on Heat Kernels	1	(28)
S. Aida
Feynman Integrals Associated with Albeverio-Hoegh-Krohn and Laplace Transform Potentials	29	(20)
N. Asai
I. Kubo
H.-H. Kuo
Random Iteration of I.I.D. Quadratic Maps	49	(10)
K. B. Athreya
R. N. Bhattacharya
Monte Carlo Algorithms and Asymptotic Problems in Nonlinear Filtering	59	(30)
A. Budhiraja
H. J. Kushner
A Covariant Quantum Stochastic Dilation Theory	89	(12)
P. S. Chakraborty
D. Goswami
K. B. Sinha
Interacting Particle Filtering with Discrete-Time Observations: Asymptotic Behaviour in the Gaussian Case	101	(22)
P. Del Moral
J. Jacod
Hidden Markov Chain Filtering for Generalised Bessel Processes	123	(22)
R. Elliott
E. Platen
On the Zakai Equation of Filtering with Gaussian Noise	145	(8)
L. Gawarecki
V. Mandrekar
Prediction and Translation of Fractional Brownian Motions	153	(20)
Y. Hu
Time Maps in the Study of Feynman's Operational Calculus via Wiener and Feynman Path Integrals	173	(22)
G. W. Johnson
L. Johnson
Two Applications of Reproducing Kernel Hilbert Spaces in Stochastic Analysis	195	(12)
T. Koski
P. Sundar
Stochastic Linear Controlled Systems with Quadratic Cost Revisited	207	(26)
N. V. Krylov
Numerical Solutions for a Class of SPDEs with Application to Filtering	233	(26)
T. G. Kurtz
J. Xiong
Nonlinear Diffusion Approximations of Queuing Networks	259	(26)
B. Margolius
W. A. Woyczynski
On Equations of Stochastic Fluid Mechanics	285	(18)
R. Mikulevicius
B. Rozovskii
Infinite Level Asymptotics of a Perturbative Chern-Simons Integral	303	(18)
I. Mitoma
Risk-Sensitive Dynamic Asset Management with Partial Information	321	(20)
H. Nagai
Existence of a Strong Solution for an Integro-Differential Equation and Superposition of Diffusion Processes	341	(20)
Y. Ogura
M. Tomisaki
M. Tsuchiya
On the Consistency of the Maximum Likelihood Method in Testing Multiple Quantum Hypotheses	361	(18)
K. R. parthasarathy
Large Deviations for Double Ito Equations	379	(22)
V. Perez-Abreu
C. Tudor
The Domain of a Generator and the Intertwining Property	401
I. Shigekawa