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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
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
The study of measure-valued processes in random environments has
seen some intensive research activities in recent years whereby
interesting nonlinear stochastic partial differential equations
(SPDEs) were derived. Due to the nonlinearity and the non-Lipschitz
continuity of their coefficients, new techniques and concepts have
recently been developed for the study of such SPDEs. These include
the conditional Laplace transform technique, the conditional mild
solution, and the bridge between SPDEs and some kind of backward
stochastic differential equations. This volume provides an
introduction to these topics with the aim of attracting more
researchers into this exciting and young area of research. It can
be considered as the first book of its kind. The tools introduced
and developed for the study of measure-valued processes in random
environments can be used in a much broader area of nonlinear SPDEs.
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