Questions tagged [stochastic-processes]
For questions about stochastic processes, for example random walks and Brownian motion.
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Why do we need \rho (utilization)<1 in queuing theory?
I’m studying basic queueing theory, in particular a single–server queue with one arrival stream and one server (a G/G/1 type setup).
Let
A be the interarrival time with mean E(A),
B be the service ...
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If a Stochastic Differential Equation is bounded [0,1], can we assume that models probability failure; [closed]
I want to model a system in terms of probability of failure. If I use a stochastic differential equation that is bounded [0,1], can I assume that it models probability failure? I know that failure ...
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Solution to SDE as measurable function of initial value
In Schilling's "Brownian Motion", it is argued in Remark 21.24 that if the stochastic process $X^x$ is the solution to an SDE with initial value $x\in\mathbb{R},ドル then it depends measurably ...
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The physical meaning of the "coupling operator" [closed]
I am reading Vassili N. Kolokoltsov's paper "On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States" and having trouble understanding the physical meaning of ...
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Convergence of Random Walk and Bounded Martingals
First, consider a symmetric random walk $X_n := Y_1 + \dots + Y_n,ドル with $P(Y_k = \pm 1) = \frac{1}{2}$ for all $k \in \mathbb{N}$. For $c > 0$ define the stopping time $T_c := \min \{n \geq 0 ,円|,円...
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A multilinear version of Cauchy-Schwarz inequality
Let $\mathbb{H}_1,\mathbb{H}_2$ be two vector spaces over $\mathbb{R},ドル and assume that we have a miltilinear function $f:\mathbb{H}_1\times \mathbb{H}_1\times \mathbb{H}_2\times\mathbb{H}_2\to \...
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Beginner question about Option pricing, Risk and Rational portfolios
I'm a physics student currently reading "Econophysics and Physical Economics by Peter Richmond, J ̈urgen Mimkes, and Stefan Hutzler" for the first time and this is my first touch with the ...
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Reversibility of a random walk
Let a random walk on a graph $G=(V,E)$ be characterized by the transition matrix $P$.
The usual discrete random walk process is:
\begin{equation}
p^{t+1}= p^{t} P,
\end{equation}
where $p^{t}$ is a ...