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Nonlinear term in the KPZ equation

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#partial-differential-equations #stochastic-processes #stochastic-calculus #stochastic-differential-equations
64
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If $(X_t)_{t\ge0}$ is a Markov process with invariant measure $\mu$, does the distribution of $X_t$ weakly converge to $\mu$ as $t\to\infty$?

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#probability-theory #measure-theory #stochastic-processes #markov-process #stochastic-analysis
28
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Reaching state N in at most n=4 steps

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#stochastic-processes
1.3k
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The distribution of a stopping time

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#stochastic-processes #martingales #stopping-times
213
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How to use $\mathbb E[(X-\mathbb E[X])^2]=\mathbb E[X^2]-\mathbb E[X]^2$ on $\operatorname{Var}(X)=0$

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#probability-theory #stochastic-processes #variance #expected-value
52
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Point-wise scaling of stochastic processes on $\mathbb{R}$

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#probability-theory #stochastic-processes #covariance
54
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Show that the composition of a sub-invariant measure with a sub-Markov kernel is a contraction on $L^p$

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#probability-theory #measure-theory #stochastic-processes #markov-process #stochastic-analysis
173
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time between transitions in continous time discrete state Markov process

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#stochastic-processes #markov-process #random-walk #random
134
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Brownian motion, stochastic process

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#stochastic-processes #brownian-motion
1.2k
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Show a Continuous Local Martingale is a Martingale

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#stochastic-processes #stochastic-calculus #martingales #stochastic-integrals #stopping-times
952
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Convergence of the distribution of the Langevin diffusion to its invariant measure

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#probability-theory #stochastic-processes #markov-process #stochastic-analysis #stochastic-differential-equations
801
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Understanding Dirichlet Process (vs Dirichlet Distribution)

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#probability-distributions #stochastic-processes
45
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Confusion about notation on continuous pathed stochastic processes

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#stochastic-processes
45
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Reflexion principle equivalence of statements

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#probability-theory #stochastic-processes #brownian-motion
33
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Approximating left continuous process $(L_t)_{0 \leq t \leq T}$ uniformly on $[0,T]$ by step functions on the Dyadics

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#probability #probability-theory #stochastic-processes #stochastic-calculus #stochastic-analysis

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