Tagged Questions

A stochastic process satisfying the Markov property: the distribution of the future states given the value of the current state does not depend on the past states. Use this tag for general state space processes (both discrete and continuous times); use (markov-chains) for countable state space ...

2answers
101 views

Markov Chains - Strong Markov Property

I'm struck with an exercise. I tried, but the results don't seem to fit to those proposed. Exercise: Two players play the following game. The one who begins draws two cards from a deck of 40 cards ...
1answer
76 views

Autocorrelated, discrete, bounded and symmetric random walk with no edge attraction

I need to move over a discrete set of linearly organized.. let's say "Japan steps" $S=\{0,\dots,c\}, c \in \mathbb{N}^*$. My current position is given by $d \in S$. On each time step, I need to draw ...
0answers
28 views

Factorization of the Fokker-Planck semigroup

"In the classical theory of Markov processes, the Fokker-Planck semigroup $\{T_t:t\ge 0\}$ can be factored as $T_t=N\circ U_t \circ j$, $t\ge 0$, where $j$ is an embedding, $U_t$ is a group of ...
1answer
40 views

Markov processes and $C_0$-semigroups

A Markov process $(X_t)_{t \geq 0}$ in continuous time on $\mathbb{R}^d$ can be described by a semigroup of Markov kernels $(p_t(x,A))_{t \geq 0}$ with $p_0(x,A) = 1_{A}(x)$ and which fulfill the ...
0answers
44 views