All Questions
37
questions
1
vote
0
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33
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Equation with the expectation of a assessed Markov process
In my book about Markov processes there is following equation in a proof and I don't see why it's right, I already ask some people in the university, but I had no success, can somebody help me?
$$E(\...
- 33
10
votes
1
answer
234
views
Exploiting the Markov property
I've encountered the following problem when dealing with short-rate models in finance and applying the Feynman-Kac theorem to relate conditional expectations to PDEs.
Let $(\Omega,\mathcal{F},\{\...
- 1,524
6
votes
1
answer
1k
views
How to Prove that a (Centered) Gaussian Process is Markov if and only if this Equation Holds?
A centered Gaussian process is Markov if and only if its covariance
function $\Gamma: \mathbb{R}\times\mathbb{R} \to \mathbb{R}$ satisfies
the equality:
$$\Gamma(s,u)\Gamma(t,t)=\Gamma(s,t)\...
- 21.3k
1
vote
1
answer
459
views
How to use the Markov property of Brownian motion
This is a problem from Durrett's probability with examples, exercise 8.2.1. It is not homework. The exercise states: Let $T_0 = \inf\{s > 0 : B_s = 0\}$ and let $R = \inf\{t > 1 : B_t = 0\}$. ...
3
votes
1
answer
640
views
Stationary Markov process properties
Let $X$ be a right-continuous process with values in $(E,\mathcal{E})$, defined on $(\Omega, \mathcal{F}_t,P)$. Suppose that $X$ has stationary, independent increments.
I now want to show the ...
user155670
1
vote
1
answer
49
views
Markov Processes: $P_x$ and $E_x$
In the study of Markov processes, one usually introduces the measures $P_{\pi}$ on the path space of the process where $\pi$ is an initial distribution of the process $X$ i.e $\pi=\mathcal L(X_0)$. ...
user153312
2
votes
1
answer
380
views
Markov property for a stochastic process with discrete state space.
Consider a stochastic process $\{X_s\}_{s\in\mathcal S\subseteq\mathbb R}$ with value in $(\mathbb R,\mathcal B(\mathbb R))$ adapted to a filtration $\{\mathcal F_s\}$ (we can suppose that $\{\...
- 13.5k