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A stochastic process is a collection of random variables usually indexed by a totally ordered set.

Let $B_t, t\geq 0$ be standard Brownian motion. Let $\big(\mathcal{G}_t, t\geq 0\big)$ be the natural filtration, defined by $\mathcal{G}_t=\sigma(B_s, 0\leq s\leq t)$. Define also a filtration $\b … asked Jul 23 '16 by James Martin 3answers Let$X_1, X_2, X_3,\dots$be an i.i.d. sequence of random variables with finite mean. Write$S_n=X_1+X_2+\dots+X_n$. Let$N$be a non-negative integer-valued random variable with finite mean.$N$may … asked Feb 22 '11 by James Martin 1answer Consider a Galton-Watson branching process, with offspring distribution$\mathbf{p}=(p_0, p_1, \dots, p_n, \dots)$. Let$O$be the root of the branching process. Write$\eta=P(\text{process survives …
asked Oct 6 '10 by James Martin
I'm interested in the following symmetric functions $s_k: \mathbb{R}_+^{k}\mapsto\mathbb{R_+}$: \begin{align*} s_k(x_1,x_2,\dots, x_k)&= \int\limits_{0=t_0<t_1<\dots<t_{k-1}<t_k=1} e^{-(t_1-t_0) x_1} …
asked Oct 10 '16 by James Martin

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