# Tagged Questions

Questions on the calculus of stochastic processes, or processes that have a random component.

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### Uniqueness of Brownian motion

May be it is a dumb question, but it vexed me a little bit. I understand the construction of the Brownian motion (first use Kolmogorov extension theorem to construct value at dyadic times and then use ...
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### How to calculate the PSD of a stochastic process

Say we have a stochastic process described by a stochastic differential equation (in the Itô sense), and maybe we are able to find an explicit solution of it in terms of deterministic and Itô ...
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### Higher math and statistics/probability

So I've heard that certain areas of statistics and probability use manifolds and results from analysis and topology. Given that I lack the background to see where manifolds would become useful in ...
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I would like to know if $B_t=W_t-\int_0^t \frac{W_u}{u}du$ is a brownian motion. I know that $W_t$ is a brownian motion. For that i would like to use Levy's characterization, so I have to show that $[... 0answers 38 views ### costruction of brownian motion on sphere? i am trying to construct a brownian motion on the sphere using the method given in Price and williams paper.$\partial$represents the SDE of stratonovich type which is converted to ito form in last ... 0answers 27 views ### Finding the mean of$X_t = \int_0^t sW_sdW_s$For the stochastic integral, where$W_t$is a Wiener process, I am trying to find the mean of$X_t = \int_0^t sW_sdW_s$. I have read before that any stochastic integral with$dWt$has mean zero, but I ... 0answers 36 views ### Generating a list of numbers A set of numbers is generated starting from$0$in the following way: Add the current number to the resultset In a chance of 50:50, do Either add$2$to the current number Or subtract$1$from the ... 0answers 44 views ### The limit of the ratio of two stochastic integrals I am just wondering how to calculate the limit of stochastic integrals. Here is one example: $$\lim\limits_{N \rightarrow \infty}\dfrac{\int_{0}^{N}B(s)dB(s)}{\int_{0}^{N}B^2(s)ds}$$ where$B(s)$is ... 0answers 56 views ### conversion from stratonovich SDE to Ito's form? conversion of stratonovich SDE to Ito SDE (Where$\partial$is differential in the stratonovich form and$d\$ is in ito's form): $$\partial X_t=\sigma(X_t,t)\partial B_t+b(t,X_t)\partial t$$. ...
I am currently working on to derive the following form of the stock price dynamics: $$dS_t = S_t[(r_t + \psi\sigma_S)dt + \rho \sigma_S dz_{1t} + \sqrt{1-\rho^2}\sigma_S dz_{2t}$$ where the ...