Stroock-Varadhan support theorem for random evolution equation in Besov-Orlicz spaces
Keyword(s):
We consider the family of stochastic processes $X=\{X_t, t\in [0;1]\}\,,$ where $X$ is the solution of the It\^{o} stochastic differential equation \[dX_t = \sigma(X_t, Z_t)dW_t + b(X_t,Y_t) dt \hspace*{2cm}\] whose coefficients Lipschitzian depend on $Z=\{Z_t, t\in [0;1]\} $ and $Y=\{Y_t, t\in [0;1]\}$. We prove that the trajectories of $X$ a.s. belong to the Besov-Orlicz space defined by the f nction $M(x)=e^{x^2}-1$ and the modulus of continuity $\omega(t)=\sqrt{t\log(1/t)}$. The aim of this work is to characterize the support of the law $X$ in this space.
2020 ◽
1990 ◽
Vol 19
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pp. 65-70
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2020 ◽
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pp. 25-31
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pp. 149-153
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2016 ◽
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pp. 1-8
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