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Confusion about the difference of quadratic variations and the Lebesgue-Stieltjes Integral

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#integration #stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
116
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Solving $\int X_s \, ds = B_1$ where $B$ is a Brownian motion

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#real-analysis #probability-theory #stochastic-processes #stochastic-calculus #stochastic-analysis
370
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Prove $ X_{t}=e^{W_{t}}-\frac{1}{2} \int_{0}^{t} e^{W_{s}} \mathrm{d} s $ is a martingale

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#stochastic-processes #stochastic-calculus #brownian-motion #martingales
185
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Does this martingale representation hold?

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#stochastic-processes #stochastic-calculus #martingales #stochastic-integrals
73
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Application of Ito formula to $\exp(-\int_t^T f(t,u)du)$

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#stochastic-processes #stochastic-calculus #finance #stochastic-integrals #stochastic-analysis
71
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2d-Brownian Motion hitting a specific point

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#probability #stochastic-processes #stochastic-calculus #brownian-motion
4.2k
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Using Ito Isometry formula

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#stochastic-processes #stochastic-calculus #stochastic-analysis
30
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Inclusion of stochastic processes classes

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#probability #stochastic-processes #stochastic-calculus #expected-value
107
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Given λ > 0 compute the expectation of the following expression

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#stochastic-calculus #expected-value #stochastic-integrals #stochastic-differential-equations
55
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Quadratic variation of two processes

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#stochastic-processes #stochastic-calculus #stochastic-integrals
203
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Is the partial derivative of a stochastic integral well defined?

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-integrals
2k
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Is the Ito integral a martingale?

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#stochastic-calculus #martingales #stochastic-integrals
98
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When is a this stochastic integral a Martingale, stopping time in the integral.

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#stochastic-calculus #martingales #stochastic-integrals #stochastic-analysis #local-martingales
80
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SDE, How to calculate and check the result

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#derivatives #stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-differential-equations
181
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What are the processes whose second moment equal their quadratic variation (like the Brownian motion)?

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-analysis #quadratic-variation

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