Reviews of the World Scientific book on spatial branching: 

• "The book is well-written. I enjoyed reading it thanks both to the contents and the attractive style of presentation. The author has invested a lot of efforts to present highly nontrivial results in a clear and understandable way. Many assertions are followed by informal discussions intended to lead the reader into the core of problems." -- Zentralblatt MATH

• "Overall, I would think the volume will make a useful addition to the libraries of either those working in the area of spatial branching processes or those looking to learn more about it."-- AMS Math Reviews 

Review of the second World Scientific book (with Volkov) on inhomogeneous Markov chains: 

"The authors have chosen an appropriate title well corresponding to the content of the book. In fact, this is a modern monograph on inhomogeneous Markov chains. Interesting stochastic models are treated and good questions are asked, followed by answers and proofs. It is a pleasure to read the book and get a satisfaction by the smooth and elegant way of passing from one concept or model to another one. The authors of this book have published a series of original papers in top journals, so their contribution is new, fresh and essential. Moreover, other scientists followed and further studied some of the models. It is great to see most recent developments in this area carefully collected and well presented now in a monograph form.

The book follows more or less established good traditions. In Chapter 1 we find notions such as Lévy’s Borel-Cantelli lemma, anti-concentration inequalities of Kolmogorov, Rogozin and Kesten, basics of martingales, moment problems and point processes and measures. Chapter 2 is dealing with time-homogeneous Markov chains: Chapman-Kolmogorov equations, transience and recurrence properties, reversibility, total variation convergence. Chapter 4 is explaining some difficulties arising when we study inhomogeneous Markov chains. Thus we arrive at two of the main chapters, 4 and 5, entirely devoted to “Coin Turning”. The authors tell first intuitively, then strictly, what does this term mean: it is a time-inhomogeneous Markov chain with just two states, 𝖲={T,H}, or 𝖲={0,1}. The idea is to follow an action called “turn over”. It only looks that this model is elementary, however, there is a list of questions to ask which need serious efforts to find the answers. A lot of stuff from discrete probability is involved and special functions from analysis are needed. Several beautiful results are presented with their detailed proofs. One can see the difference when studying the three cases, critical, supercritical and subcritical. It is shown that the coin-turn random walk obeys interesting properties while the scaled random quantities satisfy the WLLN. Urn models and related time-inhomogeneous Markov processes are treated in Chapter 7. Moreover, the urns’ specifics are combined with the coin-turning. Rademacher random walks are considered in Chapter 8. More advanced material, e.g., coin-turning random walks in higher dimensions, is included in the last two chapters, 9 and 10. The authors study a class of conservative random walks and urn-related random walks with specific drift. Recurrence, transience, and multidimensional scaling limits are studied.

There are useful graphical illustrations to some concepts and results. At the end of each chapter there are exercises with short hints and, in a couple of cases, historical notes. The bibliography looks exhaustive as is also the subject index.

In brief, this monograph is a great addition to the collection of fundamental sources in modern theory of stochastic processes. Any scientist in this area would find novelties eventually inspiring further studies. The book can be used as a source for a special advanced course addressed to university MSc and PhD students.

It can be predicted that the monograph will be well-met by the stochastics community. Many individuals may find deserving to have own copies, however, the monograph must be available in any Math Library."  -- Zentralblatt MATH

Comments and errate to books:

1. Comments and errata to the branching WS book: CLICK       

2. Comments and errata to the Markov chin WS book (with Volkov): CLICK 

The e-book format of the first WS book: