I was born in the city of Lvov, near the geographical centre of Europe, which is midway between Rome and Moscow (claimed to be the third Rome). This ancient Russ-Polish-Jew-Ukranian town is better known among mathematicians as the home of the Scottish Café. The famous Scottish Book with open mathematical questions originated in that café during the creation of functional analysis, when Steinhaus "had Banach as the first and Lebesgue as the last doctoral candidate" appointed in Lvov.
My father who was Russian was sent to Lvov and then appointed as a lecturer at a technical school there after it had become part of the Soviet Union as a result of the outbreak of the second world war. My mother was born in Lvov, as was my grandmother, who had lived in Austria, Russia, Galicia, Poland, Soviet Union, Germany, and then Soviet Ukraine, although she had never moved from Lvov and crossed any borders!
In school I was lucky to have the same teacher of physics for 5 years who was always asking me to solve new problems at the blackboard immediately after his lecture, and who encouraged me to participate in many Olympiads on mathematics and physics. His enthusiasm and optimism developed my interest in mathematical physics. Only later I learnt that he had attended Banach and Kuratowski lectures with a fellow student Mark Kac but had to give up the graduate studies because of the war.
After winning at the Whole-Ukraine Olympiad at the finish of school with the Silver Medal, I was recommended to study at Moscow State University which had at that time the best school of mathematics and mathematical physics in the world.
I passed successfully all five highly competitive entrance exams, and was admitted to do a six year Master course with further specialisation in then new physical mathematics and mathematical cybernetics including apart of theoretical physics mathematical logics, information and communication theory, automata, filtering and control, statistics, and quantum optics and radiophysics. I was lucky again to find excellent supervisors and teachers: Boris Grishanin and then Rouslan Stratonovich, who had already written three monographs and over hundred papers, quickly introduced me into their research and became my friends.
I graduated from MSU in 1970 with two already published and two submitted papers on information theory, quantum measurement and estimation, and got an award (gold watch and diploma) for the best diploma project of the year. This gained me a scholarship to continue my research for a PhD degree in statistical and quantum physics under Professor Stratonovich supervision. My thesis "Optimal measurement and estimation for quantum communication" was defended in less than three years with seven publications. In spring 1973 I was invited by Professor Maslov to join him in a newly open Chair of Applied Mathematics in MIEM, now named as Moscow Institute of Electronics and Mathematics.
In summer 1973 I presented a paper on quantum information theory in my first International Symposium in Tallin, Estonia. I met Professor Helstrom, from USA, the pioneer of quantum communication, who was speaking fluent Russian. He struck me by saying that he had started to learn Russian just 6 months ago in preparation for this meeting and that he had translated 3 of my papers into English to publish them in America. My English was poor; I was studying German at school, so I decided to study English too by translating my other papers.
In the MIEM my career initially was very successful: by the third year I was already promoted to a Senior Lecturer, and I received the position and title of Docent (equivalent to Associated Professor or Reader) in another two years. I was continuing my research on quantum measurement, mathematical statistics and communication, and by 1978 I had already published a few dozens of papers. But instead of writing up a dissertation for the higher doctoral degree (equivalent to German habilitation and a necessary condition for getting Chair) I decided to take a leave for study the Quantum Stochastic Processes, a new field in the rapidly developing Theory of Quantum Probability. I was particularly interested in the Quantum Measurement Process: I had a feeling that I could resolve the Quantum Measurement Problem in continuous time by constructing a quantum stochastic process of continual observation in a quantum open system. Then I would apply the Stratonovich nonlinear filtering method to derive the notorious quantum reduction s imply as a result of the stochastic evolution of quantum posterior state.
I received a scholarship for one year from the Ministry of High Education of Russia and went to Poland, the first foreign country in my life. Professor Ingarden invited me to work at the Copernicus University in his recently created Quantum Probability Chair. I wanted also to go to Dublin, Rome or Heidelberg but I was lucky to be allowed to go to Torun', because not being a Communist Party member it was extremely difficult to get permission for study abroad, and almost impossible to do it in a capitalist country. There I met Professor Kossakowski who had just published his Lindblad form of the quantum Markov generator that I discovered independently before leaving Russia. During the polish year 1978/79 I studied Markov semigroups and quantum entropy on C* and von Neumann algebras and took a part in several international meetings. Some results of this study were prepared and published with the help of my polish friend Przemyslaw Staszewski, who became my collaborator and was later awarded a PhD in this subject.
After returning to Moscow I spent a great deal of effort on the development of the general theory of quantum stochastic processes. I obtained a non-commutative analogue of the Kolmogorov's Main Reconstruction Theorem for general quantum stochastic processes and covariant quantum relativistic fields. It was difficult to publish anything like this at that time, and my paper, with proof of this theorem, was accepted only after three years of struggle with a referee, whose main argument in the end was that a similar theorem was going to appear soon somewhere in the West! My theorem was published after the appearance of the rival paper by Accardi, Frigerio and Lewis when I got a possibility to prove the advantage of my own approach, later rediscovered by Bhat and Parthasarathy, in the seminar of Dobrushin, Minlos and Sinai, after I received a signed support of the great Kolmogorov!
At that time Perestroika had just begun, and in the spring of 1985 I was allowed (to my great surprise) to visit Italy: I was invited by Professor Dinner from Paris to deliver two lectures at a conference in Udine on Informational Complexity in Quantum Physics. He offered me full financial support of travel from the Louis De Broglie fund. I was completely flattered when Professor Dinner, the Director of the De Broglie Fundation, showed me a folder containing the full collection of my papers.
In the same year I was invited by Professor John Lewis to visit the Dublin Institute of Advanced Studies, but I was told that my research visits abroad wouldn't be allowed more often than once in two years. In the meantime I wrote a series of papers on quantum point processes and nonlinear CP semigroups for quantum branching processes, and I started to work on quantum stochastic calculus which was under intensive studying in Nottingham by Hudson and Parthasarathy. I desperately needed it for a stochastic description of quantum continual measurements and for the derivation of the quantum continuous reduction equation which would give a dynamical solution of the quantum collapse problem.
After visiting Dublin in 1987 where I gave a series of lectures on quantum Markov semigroups and nonlinear kinetic equations I received an invitation to present a lecture at the Bellmann Continuum Conference in France on quantum nonlinear filtering and control. But I hadn't yet developed this theory, I was just thinking about how to derive the nonlinear filtering equation fom a quantum Lagevin equation! Within a week or so of hard work I obtained this equation and submitted the paper to the conference at the end of 1987. At last I could get it as I had found a new unifying algebraic approach to quantum stochastic integrals and differential equations in the most general form. I spent all of 1988 improving these important results in-between giving talks and invited lectures at different universities and conferences in Poland, France, Italy and Russia.
At the end of the year I went to Torun where, with the help of Dr Staszewski, I wrote up 10 papers in one month all of which were finished during 1989 and eventually published elsewhere. By the end of 1989, the last part of which I spent in Italy, I could already count over 20 written papers. This was the most productive year in my life. At the beginning of 1990 I was invited to Nottingham for four months to work with Professor Hudson, and the rest of the year I spent travelling and working at different universities in Poland, Germany, Switzerland, France and India. I was also invited by the University of Rome and two universities in Germany to take the chairs of Guest Professor, but I decided to postpone the tempting offers of 100 times increase of my salary. Although it was already not actual, I wanted to defend my habilitation in Russia that I was supposed to do at least 10 years earlier.
I had already decided that I would leave the Soviet Union before its split: I did not believe in Perestroika and felt it would soon collapse. My thesis "Quantum Stochastic Integration and Filtering" defended at Steclov Mathematical Institute in Moscow in 1991, was examined by top academicians from three Soviet Republics: Sinai from Russia, Skorohod from Ukraine and Grigolionis from Lithuania, and this was the last such collaboration of its kind between the separating academia. I was immediately promoted to full professor in my home institution but it was too late. On the 1st December of 1991, the day of Referendum for Independence in the Ukraine, I left the Soviet Union for Germany and then England, just a few days before it collapsed. I was not searching carefully for permanent positions in the West but took the first offer of a lectureship at Nottingham while I was Guest Professor at Marburg in 1992. After visiting some universities in USA in early 1992 I decided that Europe was a better place to live and work, and England was even better. I had liked the university in Nottingham when I visited it the first time in 1990, and I had good friends and a group to work with. I was hoping for a quick promotion, but it took me almost five years. I was promoted directly to the Chair when I received the Russian State Prize and Gold Medal.