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Stochastic ordinary and partial differential equations generalize the concepts of ordinary and partial differential equations to the setting where the unknown is a stochastic process.

1 vote
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Different solution to system of nonlinear second order ODEs

Given the system of the following two ODEs $$0=\frac{1}{2} \sigma^{2} \Phi_i''\left(x\right)+\left(\mu-\tilde{K} \Phi_1'(x)-\tilde{K} \Phi_2'(x)\right)\ \Phi_i'\left(x\right)-\delta \Phi_{i}\left(x\r …
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2 votes

Law of OU process with time-dependent dynamics

As (assuming $\Sigma\in L^2([0,\infty))$ $$ m_t=\mathbb{E}[X_t] = x + \int_0^t [M_s^1+M_s^2\mathbb{E}[X_s]] ds $$ by the fundamental theorem of calculus, the right hand side is differentiable in $t$, …
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