Physical Sciences and Mathematics Commons^™

On Markov Processes Charecterised Via Martingale Problem., Abhay G. Bhatt Dr.

Doctoral Theses

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)) – ∫t0 Lf(X(s))dsis a martingale for every f ∈ D(L). i.e. X is a solution to the martingale problem …