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Expected Growth of General Pure Birth Process

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#stochastic-processes #markov-chains #markov-process #birth-death-process
117
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Proving $\sqrt{\operatorname{Var}(\int_0^t\Phi(s)\,\mathrm ds)}\le\int_0^t\sqrt{\operatorname{Var}\Phi(s)}\,\mathrm ds$

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#inequality #stochastic-processes
382
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If $X_n$ is a submartingale, and $M,N$ are stopping times with $M \leq N$, then $X_M \leq E(X_{N} \mid \mathcal{F}_M)$

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#probability #probability-theory #stochastic-processes #conditional-expectation #martingales
62
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What is the distribution of the number of objects in each bin when we have C bins and N objects?

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#probability #probability-theory #probability-distributions #stochastic-processes
207
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Sum of compound Poisson processes with dependent counting process

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#probability #reference-request #stochastic-processes #actuarial-science
382
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Independent Increments of Time Integral of Brownian Motion

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#real-analysis #stochastic-processes #stochastic-integrals #stochastic-analysis
388
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How to show $X_{t}$ is a solution to a stochastic differential equation?

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#probability #probability-theory #stochastic-processes #stochastic-calculus #stochastic-integrals
147
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How can I find the distribution of an itô diffusion given it's generator?

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#stochastic-processes #stochastic-differential-equations
306
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Hitting time of a sphere by a Brownian particle

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#probability-theory #reference-request #stochastic-processes #brownian-motion #heat-equation
40
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Does the specific sequence of random variables converge almost surely to a given constant?

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#probability #convergence-divergence #stochastic-processes #random-walk #almost-everywhere
95
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Weak convergence in $C([0,+\infty))$ and convergence in probability

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#probability #probability-theory #stochastic-processes #weak-convergence
254
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Is there a definition for a matrix Gaussian process?

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#probability-distributions #stochastic-processes
764
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The transformation from Ito integral to Stratnonvich integral

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#stochastic-processes #stochastic-calculus #stochastic-integrals
33
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Show the derivability of a process using Itô's lemma

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#stochastic-processes #stochastic-integrals
83
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Maximum size of a subcritical birth-death process

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#probability-theory #stochastic-processes #markov-chains #birth-death-process

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