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Show that $Z(t)=\exp{\sigma X(t)-(\sigma \mu + \frac{1}{2} \sigma^2)t}$ is a martingale

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#stochastic-processes #stochastic-calculus #brownian-motion #martingales
111
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Infinitesimal generator of Brownian motion on the unit sphere

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-analysis
75
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How do you know if something satisfies a Stochastic Differential Equation?

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#calculus #stochastic-calculus #stochastic-differential-equations
67
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Is continuous, uniformly integrable martingale indistinguishable from BMO martingale?

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#stochastic-processes #stochastic-calculus #conditional-expectation #martingales #stochastic-analysis
59
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Meaning of the terms in the infinitesimal generator formula

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-analysis
46
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Computing expected value of hitting time for a Feller process

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#probability-theory #stochastic-processes #stochastic-calculus #martingales #markov-process
26
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Derivative of the quadratic variation of Levy process

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#stochastic-processes #stochastic-calculus #levy-processes #quadratic-variation
36
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Correcting term to variance OU process when using Euler Maruyama and time step of 1

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#stochastic-processes #numerical-methods #stochastic-calculus
19
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Understanding the sum of Bernoulli variables, and functions defined on such sums.

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#probability-theory #stochastic-processes #random-variables #stochastic-calculus #bernoulli-distribution
26
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Application of some estimate to stopped process

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#stochastic-processes #stochastic-calculus
192
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What is the formula for the Mode of the Log-Normal distribution followed by the Geometric Brownian Motion?

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#probability-theory #stochastic-processes #expected-value #stochastic-calculus #stochastic-analysis
25
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Some Questions About Covariation Calculation

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#stochastic-calculus #stochastic-integrals #stochastic-analysis
185
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Girsanov-type Theorem that alters the variance of a Wiener process

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#measure-theory #stochastic-processes #stochastic-calculus #stochastic-analysis #girsanov-theorem
39
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Prove equality without Ito's formula

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#solution-verification #stochastic-processes #stochastic-calculus
45
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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

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