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

Precise Gaussian Lower Bounds on Heat Kernels.- Feynman Integrals Associated with Albeverio-Hoegh-Krohn and Laplace Transform Potentials.- Random Iteration of I.I.D. Quadratic Maps.- Monte Carlo Algorithms and Asymptotic Problems in Nonlinear Filtering.- A Covariant Quantum Stochastic Dilation Theory.- Interacting Particle Filtering with Discrete-Time Observations: Asymptotic Behaviour in the Gaussian Case.- Hidden Markov Chain Filtering for Generalised Bessel Processes.- On the Zakai Equation of Filtering with Gaussian Noise.- Prediction and Translation of Fractional Brownian Motions.- Time Maps in the Study of Feynman's Operational Calculus via Wiener and Feynman Path Integrals.- Two Applications of Reproducing Kernel Hilbert Spaces in Stochastic Analysis.- Stochastic Linear Controlled Systems with Quadratic Cost Revisited.- Numerical Solutions for a Class of SPDEs with Application to Filtering.- Nonlinear Diffusion Approximations of Queuing Networks.- On Equations of Stochastic Fluid Mechanics.- Infinite Level Asymptotics of a Perturbative Chern-Simons Integral.- Risk-Sensitive Dynamic Asset Management with Partial Information.- Existence of a Strong Solution for an Integro-Differential Equation and Superposition of Diffusion Processes.- On the Consistency of the Maximum Likelihood Method in Testing Multiple Quantum Hypotheses.- Large Deviations for Double Itô Equations.- The Domain of a Generator and the Intertwining Property.