# Tagged Questions

35 views

### Question regarding Notes on Strong Markov Property

I wrote the following notes from a lecture a couple of weeks ago and I don't understand a particular line. Suppose $B_t$ is a Brownian Motion. Now look at $B^x_t = x + B_t$ which is a BM starting ...
Consider $L$ the operator forming as $$Lg= -g^{'}(x)+(g(x+1)-g(x))$$. $h$ on $[0,\infty)$ satisfies the following integro-differential equation $$Lh \geq 0$$ with boundary condition: $$... 1answer 51 views ### Markov processes and semimartingales Semimartingales and Markov processes are two fundamental families in probability theory. There are many specific processes that belongs to the intersection of those two families, e.g. Levy processes. ... 2answers 268 views ### Diffusion process. Distribution vs transition probability. I need confirmation on the following problem: Take a SDE of the form: $$dX_t=a(X_t,t)dt+b(X_t,t)dW_t$$ where all the conditions, such that the solution X_t is defined ... 1answer 403 views ### Motivation of Feynman-Kac formula and its relation to Kolmogorov backward/forward equations? Kolmogorov backward/forward equations are pdes, derived for the semigroups constructed from the Markov transition kernels. Feynman-Kac formula is also a pde corresponding to a stochastic process ... 1answer 466 views ### Multidimensional infinitesimal generator of a jump-diffusion Let X=\{X_t\}_{t\geq0} be an n-dimensional Markov process, defined by the SDE$$dX_t = \mu(t, X_t) \, dt + \sigma(t,X_t) \, dB_t+\beta(t-,X_{t-}) \, dN_t, where $\mu, \sigma$ and $\beta$ are ...
I'm trying to prove that Brownian motion absorbed at the origin is a Markov process with respect to the original filtration $\{\mathcal{F}_{t}\}$. To be more specific, let \$(B_{t},\mathcal{F}_{t})_{t ...