Geodesic
On the exact order of growth of solutions of stochastic differential equations with time-dependent coefficients
Teoriâ slučajnyh processov, Tome 16 (2010) no. 2, pp. 12-22

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We study the exact order of growth of the solution of the stochastic differential equation $d\eta (t)=g \left(\eta (t)\right)\varphi (t)dt +\sigma \left(\eta (t)\right)\theta (t)dw(t),$ $X(0)=b,$ where $w$ is the standard Wiener process, $b$ is a nonrandom positive constant, $g$, $\sigma$ are continuous positive functions, and $\varphi$ and $\theta$ are real continuous functions such that a continuous solution $\eta$ exists. As an application of these results, we discuss the problem of asymptotic equivalence for solutions of stochastic differential equations.
Keywords: Exact order of growth
Mots-clés : equivalent solutions. 
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     title = {On the exact order of growth of solutions of stochastic differential equations with time-dependent coefficients},
     journal = {Teori\^a slu\v{c}ajnyh processov},
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     year = {2010},
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V. V. Buldygin; O. A. Tymoshenko. On the exact order of growth of solutions of stochastic differential equations with time-dependent coefficients. Teoriâ slučajnyh processov, Tome 16 (2010) no. 2, pp. 12-22. http://geodesic.mathdoc.fr/item/THSP_2010_16_2_a2/