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How can these two Feynman-Kac formulas be equivalent?

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#stochastic-calculus #mathematical-physics
332
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How to solve $ \frac{dS(t)}{S(t-)}=\mu dt+\sigma dW(t)+d\left( \sum_{i=1}^{N(t)}\left( V_{i}-1\right) \right) $

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-differential-equations #levy-processes
32
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Defining discrete stochastic integrals in infinite sum for uniformly bounded simple processes

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#probability-theory #stochastic-processes #stochastic-calculus #martingales #stochastic-integrals
1.4k
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How to compute integrals of functions of Brownian Motion with respect to time and Brownian motion?

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#stochastic-calculus #brownian-motion #stochastic-integrals
340
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Integral of $W_t$ with respect to $dW_t$ by first principles

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-integrals #stochastic-differential-equations
60
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Integral of Brownian motion over $[0,1]$

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#probability-theory #stochastic-calculus #brownian-motion #stochastic-integrals
31
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Expectation of a series of indicators function

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#probability #probability-theory #stochastic-processes #stochastic-calculus
175
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Ito's formula application

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#probability #stochastic-processes #stochastic-calculus #martingales #stochastic-integrals
309
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Stochastic process which is not a martingale

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#probability #stochastic-processes #stochastic-calculus #martingales
67
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Stopping times algebra

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#stochastic-processes #stochastic-calculus #martingales #stopping-times
173
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Notation in SDEs : angle brackets

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#integration #notation #stochastic-calculus #finance #stochastic-differential-equations
233
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Expectation of exponential of Ito Integral

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#exponential-function #stochastic-calculus #stochastic-integrals #stochastic-analysis
48
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Finding mean-square convergence of a stochastic process

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#limits #stochastic-processes #stochastic-calculus #stochastic-analysis
1.4k
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Generated Sigma Algebras

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#probability-theory #measure-theory #stochastic-calculus #finance
101
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Integrating $dX_t=-\beta X_t dt + dW_t$

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#stochastic-processes #stochastic-calculus #stochastic-integrals #stochastic-analysis #stochastic-differential-equations

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