Random Times for Markov Processes with Killing

Round 1

Reviewer 1 Report

Some remarks and suggestions:

Line 7 and 9: Gikhman and Sjorokhod is repeadt twice as well as Bochner

Formula (1): specify that you are assuming no drift and killing rate

line 75: replace "on the jumps of S" with "determined by the jumps of S"

line 96-97: introduce V more precisely by adding some details on the poisson measure, maybe provide a reference

Author Response

We thank the referee to point out some misprints and suggestions:

1. "Line 7 and 9: Gikhman and Sjorokhod is repeadt twice as well as Bochner"

We have corrected the duplications.

2. "Formula (1): specify that you are assuming no drift and killing rate"

We have mentioned that in fact we are assuming no drift and no killing rate in fact.

3.  "line 75: replace "on the jumps of S" with "determined by the jumps of S"

We have introduced the suggested improvement.

4. "line 96-97: introduce V more precisely by adding some details on the poisson measure, maybe provide a reference"

We added a classical reference on Poisson measures on configuration spaces.

Reviewer 2 Report

The authors investigated the random times for Markov processes with killing. This paper has clear logic, a reasonable derivation process, and standard language organization. The subject is interesting and the research results show the authors’ experience in this field. Therefore, it is suggested to be accepted after some Minor Revisions. Some suggestions are presented as follows:

(1) Should the ‘Abstract’ of the article be further enriched? As the authors stated that “The aim of this paper is to show how random time changes may be introduced in these Markov processes with killing potential and how these changes may influence the time behavior of them.” Perhaps a fuller ‘Abstract’ would help readers quickly grasp the main content of this paper.

(2) I don’t know why some equations in this paper have labels whereas others don’t. What are the criteria for deciding this question?

(3) Since there exist many symbols in this paper, is it necessary to present a “Nomenclature” in the paper? Maybe it is useful to help readers understand the theoretical derivation process.

Frankly speaking, the above revisions are not mandatory, but from the point of view of communicating with the authors.

Author Response

We would like to thank the anonymous referee for the suggestions to improve the quality of the paper. 

We have improved the Abstract and added a new section at the end about conclusions. Minor English improvements were done, all the changes are colored.

(1) We have improved the Abstract such that the reader has a quick grasp of the paper contents.

(2) We have numbered only equations which are cited during the text.

(3) A "Nomenclature" could help the reader. On the other, the paper is not too long and the core notation are introduced in Sections  2 and 3, we think that the paper is readable without the "Nomenclature".

Reviewer 3 Report

The article deals with a very interesting topic. The structure of the article is correct. The authors clearly define the aim of the study against the background of the achievements so far.
The presentation of the proposed solution is clearly presented. Examples of the presented solution are presented.
In my opinion, it is worth adding a chapter ending and summarizing the research carried out. This is what I miss in the reviewed article. One should briefly refer to the results and the aim of the study set out in the introduction.

Author Response

We have added a final section with the conclusions where we summarize the obtained results. Minor english corrections were introduced and they are shown in color.