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Polar Brownian motion not recovering polar Laplacian?

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#partial-differential-equations #stochastic-processes #brownian-motion #laplacian #stochastic-differential-equations
280
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Uniqueness of the parameters of an Ito process, given initial and terminal conditions

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#stochastic-processes #brownian-motion #stochastic-differential-equations
235
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$dX_t=\alpha X_t \,dt + \sqrt{X_t} \,dW_t, $ with $X_0=x_0,\,\alpha,\sigma>0.$ Compute $E[X_t] $ and $E[Y]$ for $Y=\lim_{t\to\infty}e^{-\alpha t}X_t$

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-differential-equations
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Initial Distribution of Stochastic Differential Equations

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#probability-theory #stochastic-processes #brownian-motion #stochastic-analysis #stochastic-differential-equations
44
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(In)dependence of solutions to certain SDEs

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#probability-theory #stochastic-processes #stochastic-calculus #stochastic-differential-equations #levy-processes
151
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Expectation, supremum and convergence.

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#probability-theory #stochastic-processes #expectation #stochastic-calculus #stochastic-differential-equations
338
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Integral of a sum dependent on the variable of integration

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#integration #summation #stochastic-differential-equations #point-processes
236
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Solving of enhanced Hull-White $dX_t = \frac{e^t-X_t}{t-2}dt + tdW_t$

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#probability-theory #stochastic-calculus #brownian-motion #stochastic-integrals #stochastic-differential-equations
224
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Closed form of a SDE

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#stochastic-calculus #stochastic-differential-equations
125
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Matricial form of multidimensional GBM

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#matrix-equations #stochastic-differential-equations
136
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Solve SDE and its formal solution

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#integration #stochastic-calculus #stochastic-integrals #stochastic-differential-equations
2.7k
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How to solve the SDE: $dX_t = aX_t dt + b \sqrt{X_t} dW_t$

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#stochastic-processes #stochastic-calculus #brownian-motion #stochastic-integrals #stochastic-differential-equations
96
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Compute the expectation of this stochastic process

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#expectation #stochastic-calculus #stochastic-integrals #stochastic-differential-equations
228
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Riemann integral of discrete white noise

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#stochastic-calculus #stochastic-integrals #riemann-integration #stochastic-differential-equations #noise
136
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What is the solution to SDEs of the form $dx=f(x)(dt+\rho dW_t)$?

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

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