#### Date of Submission

10-22-1992

#### Date of Award

10-22-1993

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Computer Science

#### Department

Theoretical Statistics and Mathematics Unit (TSMU-Delhi)

#### Supervisor

Karandikar, Rajeeva L. (TSMU-Delhi; ISI)

#### Abstract (Summary of the Work)

Martingale approach to the study of finite dimensional diffusions was initiated by Stroock-Varadhan, who coined the term martingale problem. Their success led to a similar approach being used to study Markov processes occuring in other areas such as infinite particle systems, branching processes, genetic models, density dependent population processes, random evolutions etc.Suppose X is a Markov process corresponding to a semigroup (T)e20 with generator L. Then all the information about X is contained in L. We also have thatMf(t) := f(X(t)) â€“ âˆ«t0 Lf(X(s))dsis a martingale for every f âˆˆ D(L). i.e. X is a solution to the martingale problem for L. Now instead of the generator L, if we start with an operator A, such that there exists a unique solution to the martingale problem for A, then under some further conditions the solution is a Markov process corresponding to a semigroup which is given by a transition probability function. Hence the operator A determines the semigroup (Tt)tâ‰¥ 0. A is then a restriction of the generator of (T)20 to D(A).

#### Control Number

ISILib-TH196

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

#### DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

#### Recommended Citation

Bhatt, Abhay G. Dr., "On Markov Processes Charecterised Via Martingale Problem." (1993). *Doctoral Theses*. 393.

https://digitalcommons.isical.ac.in/doctoral-theses/393

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843752