1
$\begingroup$

I'm looking for some good references discussing regime switching stochastic systems (Stochastic systems with markovian jump process) and their solutions.

Given a Continuous-time Markov Chain $\xi$ with state space $\mathbb S$, a regime switching stochastic sysem is given by \begin{equation} \begin{cases} dX_t&=b(t,X_t,\xi_t)dt+\sigma(t,X_t,\xi_t)dW_t\\ X_0&=x_0, \xi_0=w\in \mathbb S \end{cases} \end{equation}

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ This area is somewhat vast; for starters, see projecteuclid.org/journals/bernoulli/volume-21/issue-1/… or epubs.siam.org/doi/pdf/10.1137/… and references therein $\endgroup$
    – Nawaf Bou-Rabee
    Commented Jun 8, 2022 at 22:39
  • $\begingroup$ @NawafBou-Rabee Thank you ! $\endgroup$
    – Hamdiken
    Commented Jun 8, 2022 at 23:00
  • $\begingroup$ @NawafBou-Rabee Just checked it. My area exactly is the stochastic differential equations that depend on a markov chain $\xi$ i.e$dX_t=b(t,X_t,\xi_t)dt+\sigma(t,X_t,\xi_t)dW_t$. I couldn't access this book (amazon.com/…) so I'm looking for similar references. Thanks again ! $\endgroup$
    – Hamdiken
    Commented Jun 8, 2022 at 23:06

0

Reset to default

You must log in to answer this question.