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To find the Expectation of exponential of Brownian motion

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#stochastic-calculus #brownian-motion
270
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On the product of a stochastic integral and a random variable

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#stochastic-processes #solution-verification #stochastic-calculus #stochastic-integrals
120
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Integral w.r.t. Brownian motion vanishes when taking expectation

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#stochastic-processes #stochastic-calculus #brownian-motion
192
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Bessel process conditioned to stay positive

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis #stochastic-differential-equations
441
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Potential Local Martingale property derived from its quadratic variation

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#stochastic-processes #stochastic-calculus #local-martingales
117
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How to prove the following $L^2$ convergence

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#probability #measure-theory #stochastic-calculus
112
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Exchanging limit for Brownian stochastic integral

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#stochastic-calculus #brownian-motion #stochastic-analysis
171
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How does one derive the delta autocorrelation function for white noise?

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#stochastic-calculus #stochastic-integrals #stochastic-differential-equations
192
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How to Discretize this SDE found in finance?

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#stochastic-processes #stochastic-calculus #stochastic-differential-equations #eulers-method
96
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Confusion regarding Ito Differentiation

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#stochastic-processes #stochastic-calculus #stochastic-differential-equations
190
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Let W be a standard Brownian motion. Use Itô’s formula and induction over $n\in \mathbb{N}$ to calculate $E[W^n_t]$

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#probability-theory #stochastic-calculus #expected-value #brownian-motion
368
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Let $W$ be a standard Brownian motion, compute the stochastic integral $\int_0^t s W_s^2dW_s$. Why should I use $f(t,x)=tx^3/3$?

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#stochastic-processes #stochastic-calculus #brownian-motion #martingales #stochastic-integrals
139
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Cauchy-Schwarz for exected value of sum

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#probability #stochastic-calculus #expected-value #cauchy-schwarz-inequality
159
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Probability of sum of gaussian random variables

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#probability #normal-distribution #stochastic-calculus
115
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How do I compute this integral of standard normally distributed variables?

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#integration #normal-distribution #stochastic-calculus #gaussian-integral

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