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$E\int_0^T|X(t)|^2dt=0$ then $X=0 dP\times dt$

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#probability #stochastic-processes #stochastic-calculus #expected-value #stochastic-integrals
99
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stochastic differential equation linear diffusion coefficient

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-differential-equations
151
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Application of Girsanov's theorem

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#stochastic-processes #finance #stochastic-integrals #stochastic-analysis #stochastic-differential-equations
132
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When is the Ito representation deterministic?

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#probability #stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
142
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Find solution of stochastic differential equations

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#ordinary-differential-equations #stochastic-processes #stochastic-calculus #stochastic-integrals
218
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Use Ito formula to solve SDE

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#stochastic-calculus #stochastic-integrals #stochastic-differential-equations
166
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Quotient of continuous local martingale with quadratic variation

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#stochastic-processes #stochastic-integrals #stochastic-analysis #local-martingales
83
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Non-integer moment of some integral which is similar to the incomplete Gamma function integral

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#stochastic-calculus #martingales #gamma-function #stochastic-integrals #stochastic-analysis
109
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Write the martingale part of this semimartingale as an Itō integral process with respect to a one-dimensional Brownian motion

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#stochastic-calculus #stochastic-integrals #stochastic-analysis #stochastic-differential-equations #local-martingales
55
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Stochastic partial integration: Do the stochastic integrators have to be independent?

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis #stochastic-differential-equations
158
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Auxiliary result related to the exponential martingale inequality

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#stochastic-processes #stochastic-calculus #martingales #stochastic-integrals #stochastic-analysis
104
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Show that $\operatorname P\left[\sup_{s\in[0,\:t]}\left(M_s-\frac\alpha2[M]_s\right)\ge\alpha\beta\right]\le e^{-\alpha\beta}$

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#stochastic-processes #stochastic-calculus #martingales #stochastic-integrals #stochastic-analysis
392
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Wiener integral as a special case of Ito integral

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-integrals
176
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What is the popular way to simulate an Ito process?

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#stochastic-processes #stochastic-calculus #stochastic-integrals
59
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How to show $P(\inf_{t\geq0}\int_0^t e^{-s}\mathrm d B_s\geq -1)>0$?

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#probability-theory #probability-distributions #brownian-motion #stochastic-integrals #stochastic-analysis

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