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Find a function $b \in L^p([0,1])$ for $p \in [1,2)$ such that the laws of $W$ and $W + \int^{\cdot}_0b_s ds$ are mutually singular.

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#stochastic-integrals #stochastic-differential-equations
116
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Linear SDE with locally Lipschitz coefficients and without linear growth

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24
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Some Questions About Covariation Calculation

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#stochastic-calculus #stochastic-integrals #stochastic-analysis
44
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Find the stochastic differential equation that is solved by $e^{Y_t}$

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#solution-verification #stochastic-processes #stochastic-calculus #stochastic-integrals
40
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Missing term in Ito Integral

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#stochastic-calculus #stochastic-integrals
39
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Power Spectrum Density of cosine (or sine) of stochastic process related to Brownian Motion

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#stochastic-processes #brownian-motion #stochastic-integrals
75
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Independence stochastic integral

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis #stochastic-differential-equations
32
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Simplifying a Stochastic Integral to a Summation

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147
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Intuition - Ito's formula

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44
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Prove that $\int_0^t M_sdM_s=\frac 12 (M_t^2 - \langle M \rangle _t)$

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#stochastic-processes #stochastic-calculus #martingales #stochastic-integrals
230
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Expected value of Ornstein-Uhlenbeck process

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#stochastic-processes #stochastic-calculus #brownian-motion #finance #stochastic-integrals
107
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Why does the Yamada-Watanabe Uniqueness Theorem for SDEs not hold in the multidimensional case?

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#stochastic-calculus #brownian-motion #stochastic-integrals #stochastic-analysis #stochastic-differential-equations
54
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What is the meaning of $dX(t)$ when $X(t)$ is a random process?

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#stochastic-processes #stochastic-integrals #stochastic-analysis #stochastic-differential-equations
53
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Stochastic integral of continuous integrand with bounded variation

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
65
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Let $( W_t )$ be the standard Brownian Motion then solve $\int_0^T (W_t)^5 dW_t$

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#stochastic-processes #stochastic-calculus #stochastic-integrals

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