Stochastics in Finite and Infinite Dimensions : In Honor of Gopinath Kallianpur

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 Front Matter....Pages i-xxxvi Precise Gaussian Lower Bounds on Heat Kernels....Pages 1-28 Feynman Integrals Associated with Albeverio-Høegh-Krohn and Laplace Transform Potentials....Pages 29-48 Random Iteration of I.I.D. Quadratic Maps....Pages 49-58 Monte Carlo Algorithms and Asymptotic Problems in Nonlinear Filtering....Pages 59-87 A Covariant Quantum Stochastic Dilation Theory....Pages 89-99 Interacting Particle Filtering with Discrete-Time Observations: Asymptotic Behaviour in the Gaussian Case....Pages 101-122 Hidden Markov Chain Filtering for Generalised Bessel Processes....Pages 123-143 On the Zakai Equation of Filtering with Gaussian Noise....Pages 145-151 Prediction and Translation of Fractional Brownian Motions....Pages 153-171 Time Maps in the Study of Feynman’s Operational Calculus via Wiener and Feynman Path Integrals....Pages 173-194 Two Applications of Reproducing Kernel Hilbert Spaces in Stochastic Analysis....Pages 195-206 Stochastic Linear Controlled Systems with Quadratic Cost Revisited....Pages 207-232 Numerical Solutions for a Class of SPDEs with Application to Filtering....Pages 233-258 Nonlinear Diffusion Approximations of Queuing Networks....Pages 259-284 On Equations of Stochastic Fluid Mechanics....Pages 285-302 Infinite Level Asymptotics of a Perturbative Chern-Simons Integral....Pages 303-319 Risk-Sensitive Dynamic Asset Management with Partial Information....Pages 321-339 Existence of a Strong Solution for an Integro-Differential Equation and Superposition of Diffusion Processes....Pages 341-359 On Consistency of the Maximum Likelihood Method in Testing Multiple Quantum Hypotheses....Pages 361-377 Large Deviations for Double Itô Equations....Pages 379-399 The Domain of a Generator and the Intertwining Property....Pages 401-411 This volume, dedicated to Gopinath Kallianpur on the occasion of his 75th birthday, pays tribute to his achievements in the areas of probability and statistics, including stochastic finance.