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Quadratic variation of a multidimensional stochastic integral

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#probability #stochastic-processes #stochastic-calculus #stochastic-integrals #quadratic-variation
784
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Discretizing a Stochastic Volatility SDE

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-differential-equations
86
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Is this the definition of stochastic integral up to a stopping/explosion time?

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
822
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Problem on the exponential martingale with the Brownian motion

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#stochastic-processes #stochastic-calculus #brownian-motion #martingales #stochastic-integrals
372
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Integral of a non-negative but non-zero real-valued continuous function is strictly positive?

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#integration #probability-theory #measure-theory #stochastic-integrals
103
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Question about Protter's proof of the Ito's formula

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#probability #stochastic-calculus #stochastic-integrals #stochastic-analysis
202
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Differentiation under the integral sign for the Itō integral

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis
58
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Construction of semimartingales

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#probability-theory #stochastic-processes #stochastic-integrals #levy-processes
1.2k
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Ito's formula, and the relationship between dt and dB(t)

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#stochastic-processes #stochastic-calculus #stochastic-integrals
415
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Equality in law of two stochastic processes

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-integrals #stochastic-differential-equations
361
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solving an optimal stopping problem

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#stochastic-processes #stochastic-calculus #stochastic-integrals #optimal-control
111
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Protter: càdlàg $L^2$ Martingale is a Semimartingale

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#continuity #stochastic-processes #martingales #stochastic-integrals
2.2k
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Show that an Ito process is a martingale.

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#stochastic-calculus #martingales #stochastic-integrals #stochastic-analysis
80
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Expectation of the absolute of the difference between two B.M, $\DeclareMathOperator*{\E}{\mathbb{E}}|B(s)-B(t)|=\sqrt{\frac{2}{\pi}}|t-s|^{1/2}$?

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#expectation #stochastic-calculus #brownian-motion #stochastic-integrals
72
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Calculate the dynamics of ZCB given forward-rate dynamics

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#stochastic-calculus #stochastic-integrals #stochastic-analysis #stochastic-pde

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