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Sigma algebra generated by a set of random variables when countable

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#real-analysis #probability #measure-theory #stochastic-processes #markov-chains
50
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Application of DCT

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#measure-theory #stochastic-processes
167
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Is geometric brownian motion, $X_t + c$, shift invariant? And what is the expected value?

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#stochastic-processes #expected-value #brownian-motion #stochastic-differential-equations
113
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Showing that an entire function is dense using Brownian Motion.

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#probability #complex-analysis #solution-verification #stochastic-processes #brownian-motion
61
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Stationary distribution for random walk on $\{1,2,...,N\}$

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#probability #solution-verification #stochastic-processes #markov-chains #stationary-processes
75
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Generalised Ito Formula

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
79
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Proof of Début Theorem for right-continuous adapted process

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#stochastic-processes #stopping-times
387
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Probability for a $1$D biased random walk to reach one wall before another

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#stochastic-processes #random-walk #random #stopping-times
136
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Intuitive explanation for markov chain why a state is called aperiodic if period of state is one?

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#stochastic-processes #markov-chains
34
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For a stochastic process $X(\cdot)$ which dominates another process $Y(\cdot)$. Does equal stationary expectation imply same stationary distribution?

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#probability-theory #stochastic-processes
37
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Proof of Début Theorem for right-continuous adapted process - III

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#stochastic-processes #random-variables #proof-explanation #random #stopping-times
100
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Expectation of Mixed Exponential and Erlang Random Variables

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#stochastic-processes #random-variables #dynamical-systems #expected-value
94
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Squared Brownian motion with drift

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#stochastic-processes #stochastic-calculus #brownian-motion
108
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Jumps of a given compound Poisson process

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#probability-theory #stochastic-processes #random-variables #poisson-distribution #poisson-process
36
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Distribution of the number of trials until the last arrival in a Bernoulli process before an arbitrary point in time $t$

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#probability #probability-distributions #stochastic-processes

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