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What does "(measure) almost-every (random variable)" mean?

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#probability-theory #measure-theory #markov-process
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In a 2-state Markov chain, what is probability that $\texttt{State-2}$ has been picked exactly $k$ number of times out of $n$ timestep

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#probability #stochastic-processes #markov-chains #conditional-probability #markov-process
123
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What is this Continuous-Space Discrete-Time Markov Chain?

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#probability-distributions #stochastic-processes #markov-chains #markov-process
49
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Markov Chain - finding $P^{n}$ from graph

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#markov-chains #markov-process
44
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How can I minimize this integral functional on a function space?

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#probability-theory #optimization #stochastic-processes #lagrange-multiplier #markov-process
31
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Calculate $\operatorname E\left[\exp\left(-\int_0^tf(X_s)\:{\rm d}s\right)f(X_t)\right]$ when $X$ is stationary

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#probability-theory #measure-theory #stochastic-processes #independence #markov-process
60
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How can we simplify $\int_0^t\left.\frac{\rm d}{{\rm d}r}f(r,s)\:\right|_{r=s}\:{\rm d}s$ with $f(r,s)=\text E[g(X_r)h(X_{r+t-s})]$?

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#real-analysis #calculus #probability-theory #stochastic-processes #markov-process
66
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Expressing $\int_0^t\operatorname E_\nu\left[f(X_s)g(X_t)\right]\:{\rm d}s$ as an expectation with respect to another measure $\mu$ instead of $\nu$

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#probability-theory #measure-theory #stochastic-processes #markov-process #semigroup-of-operators
101
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How to calculate just one stationary distribution value?

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#probability #probability-distributions #markov-chains #markov-process
39
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Definition of a Markov process on the real numbers.

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#probability-theory #statistics #markov-process
360
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How to calculate the long run proportion of time spent at a certain state, given that the Markov chain starts at a different state?

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#probability #probability-theory #markov-chains #markov-process
39
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References for regularity properties of diffusion/Markov semigroups

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#partial-differential-equations #reference-request #markov-process #regularity-theory-of-pdes #semigroup-of-operators
33
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How are the variance of a Markov chain ergodic average and the variance of the corresponding continuous time embedding related?

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#probability-theory #stochastic-processes #operator-theory #markov-process #semigroup-of-operators
113
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the Probability generating functions of the first passage time in the simple random walk

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#stochastic-processes #markov-process
26
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Can we find an explicit solution of this Poisson equation?

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#probability-theory #measure-theory #operator-theory #markov-process #semigroup-of-operators

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