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Let $W_{t}$ be a Brownian motion independent of $B_{t} .$ Find the probability $P\left(\int_{0}^{1} e^{t} d B_{t}>\int_{0}^{1 / 2} t d W_{t}\right)$.

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#probability #stochastic-processes #stochastic-calculus #brownian-motion #stochastic-integrals
93
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Solve the SDE $d X_{t}=X_{t} B_{t} d t-X_{t} d B_{t}$

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-differential-equations #stochastic-pde
48
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Simulating stochastic differential equation with jumps.

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#numerical-methods #stochastic-calculus #stochastic-differential-equations #simulation
37
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Does $Y\int_a^b f(s,\cdot )dW_s=\int_a^b Yf(s,\cdot )dW_s$ ? whenever $Y$ is a random variable?

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#stochastic-calculus
85
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$E[|X|\ln(1+|X|)]<+\infty \implies \lim_k E[X|\mathcal{G}_k]=0$ a.s

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#probability-theory #measure-theory #stochastic-processes #stochastic-calculus #martingales
611
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Laplace Equation for Brownian Motion

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#probability-theory #stochastic-processes #stochastic-calculus #brownian-motion #stochastic-analysis
422
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Exponential of martingale is also martingale?

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#stochastic-processes #stochastic-calculus #martingales #stochastic-integrals
169
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Why is this a martingale (SDE)?

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#stochastic-calculus #martingales #stochastic-differential-equations
72
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Not able to see how Ito's formula is applied

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#stochastic-calculus #stochastic-analysis
88
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Find a change of time $C_{t}$ so that the following processes $M\left(C_{t}\right)$ are Brownian motion.

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-integrals
30
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SDE of translated process $X(t) + a$

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#calculus #stochastic-processes #solution-verification #stochastic-calculus #stochastic-differential-equations
236
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Dominated convergence for stochastic integrals.

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#probability-theory #stochastic-calculus #stochastic-integrals #stochastic-analysis
134
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Potential Density of Brownian local time

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-analysis #local-time
71
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What is the expected value of $\tau$?

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#stochastic-processes #stochastic-calculus #brownian-motion
339
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Is $M_t = \max_{0 \le s \le t}(B_s)$ an Itô Process?

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#probability #stochastic-processes #stochastic-calculus

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