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Quasi-diffusion solution of a stochastic differential equation

Agnieszka Plucińska, Wojciech Szymański (2007)

Applicationes Mathematicae

We consider the stochastic differential equation X t = X + 0 t ( A s + B s X s ) d s + 0 t C s d Y s , where A t , B t , C t are nonrandom continuous functions of t, X₀ is an initial random variable, Y = ( Y t , t 0 ) is a Gaussian process and X₀, Y are independent. We give the form of the solution ( X t ) to (0.1) and then basing on the results of Plucińska [Teor. Veroyatnost. i Primenen. 25 (1980)] we prove that ( X t ) is a quasi-diffusion proces.

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