# Questions tagged [stochastic-calculus]

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### Transformed Ornstein Uhlenbeck process

Say I have π that follows an Ornstein-Uhlenbeck process: $ππ_π‘=πX_tππ‘+πππ_π‘$ Let $π_π‘=exp(π_π‘)$. How can I calculate the autocorrelation function of $Y_t$?
• 1
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### Estimating jump diffusion parameters from first passage time data?

I know that there is a literature on approximating the first passage time distribution of jump diffusion processes. I know there is also a literature on estimating parameters of jump diffusion ...
• 101
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### Is it allowed to pull a stochastic variable/process outside the integral?

If we encounter an integral of the form: $I=\int\limits_0^t X(s)y(s)ds$, where $X(s)$ is a stochastic (variable or process) and $y(s)$ is a deterministic function, say $e^{as}$. I want to know under ...
• 111
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### Stochastic Process Notation / Brownian Increments

I am currently reading about stochastic processes and Brownian Motion. When books have notation such as $E[X_t] = 0$ and $Var[X_t] = \sqrt{t}$ this is considered over sample paths. However, when we ...
1 vote
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• 554
1 vote
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### what is the sensitivity of the neural network using standardized input

Suppose I trained a neural network with standardisation of the data following (X-EX)/std(X). The input is x(t) and output is y(t). How can I calculate the sensitivity of this trained network (...
• 163
1 vote
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### State dependent autocorrelation of a stochastic differential equation

I have an SDE of the form $$dX_t = f(X_t)dt + \sigma(X_t)dW_t$$ where f(x) is a rational expression. I need to compute the lag-1 autocorrelation of this process as a function of $X$. Question 1: is ...
• 81
310 views

### Let $X_t$ be a solution of a SDE. Does the set $\{X_t \in \{p\}\}$ has null measure?

This question was previously posted on https://math.stackexchange.com/questions/3981156/let-x-t-be-a-solution-of-a-sde-does-the-set-x-t-in-p-has-null-meas. I think this question is easy. However, I ...